WGU C955 Applied Probability and Statistics Quiz Bank (Latest 2023/ 2024 Update) All Modules Covered| Questions and Verified Answers| 100% Correct| Grade A
WGU C955 Applied Probability and Statistics Quiz Bank (Latest 2023/ 2024 Update) All Modules Covered| Questions and Verified Answers| 100% Correct| Grade A
WGU C955 Applied Probability and Statistics Quiz Bank (Latest 2023/ 2024 Update) All Modules Covered| Questions and Verified Answers| 100% Correct| Grade A Q: According to the strictest definition, 1/3 is… Choose only one answer below. a. an integer b. a rational number c. a real number d. All of the above Answer: a rational number Correct. The answer is b. According to the strictest definition, 1/3 is a rational number because it can be represented as a fraction. Q: -30,000 is… Choose only one answer below. a. greater than 45,000 b. less than 31,000 c. greater than 0 d. less than 50,00 Answer: 0a. greater than 45,000 Correct. The answer is a. 45,000 lies to the left of 30,000- on the numbers line a therefore is less than 30,000 Q: Which answer shows the following numbers in order from least to great- est? a. 1/3, 2/3, 1/3, 5/3 b. 1/3, 1/3, 2/3, 5/3 c. 1/3 1/3, 2/3, 5/3 d. 5/3, 2/3, 1/3, 1 Answer: /3C Q: 0, 1, 2 is a set of continuous data. True or False? Choose only one answer below.
a. True b. False Answer: False Correct. This statement is false. 00, 11, and 22 are distinct consecutive integers. There are numbers, such as 1.51.5, between them, so they are not continuous. Q: Temperature is an example of continuous data. True or False? Choose only one answer below. a. True b. False Answer: True Correct. This statement is true. Temperature covers an entire interval of data and can be “measured” rather than counted, so it is continuous. Q: Timesheets log the days that a warehouse employees work each week. Does the week’s timesheet give data that is discrete or continuous? Choose only one answer below. a. Discrete. b. Continuous Answer: Discrete Correct. The answer is a. The days of the week are discrete and do not allow for values between them. Q: A graph shows the profit margin of a particular product at two different price points. Is this data discrete or continuous? Choose only one answer below. a. Discrete b. Continuous Answer: Discrete
Correct. The answer is a. The graph shows discrete price points, not all possible prices, between two numbers. Q: A traffic monitor analyzes network usage and records upload and down- load speeds. Are these data discrete or continuous? Choose only one answer below. a. Discrete b. Continuous Answer: Continuous Correct. The answer is b. These are all continuous measurements for which it is possible to have fractional parts. Q: Which of the following is the correct translation of 3x>6? a. 10 is less than xý which is less than 6 b. 10 is less than or equal to xý which is greater than 6 c. 10 is greater than xý which is greater than 6 d. 10 is less than xý which is greater than Answer: 610 is greater than xý which is greater than 6 Correct. The answer is c. Both of the >> symbols mean “greater than,” so the correct translation is 10 is greater than xý which is greater than 6.
Q: Which of the following is the correct translation of 85 d. 9dw Answer: eb5.9ewe5 Correct. The answer is b. Both e symbols mean “greater than or equal to,” so 9ewe5 means ” w is less than or equal to 9 , but greater than or equal to 5 .” Q: How would ” x is greater than or equal to 4 , and less than 7 ” be written? Choose only one answer below. a. 4exe7 b. 4dxd7 c. 4dx<7 d. 4ex Answer:
c7. 4dx<7 Correct. The answer is c. The signs are read “less than” giving the complete answer 4 is less than or equal to x and x is less than 7. Powered by https://learnexams.com/search/study?query=
π is a __ Real number
8 2/3 is a __
rational number
12.25 is a __
rational number
111111 is a __
positive integer
−36 is a __
negative integer
77 is a __
positive integer
1/4 is a __
rational number
0.6750.675 is a __
rational number
−3/5 is a __
rational number
−1.6 is a __
rational number
True or False? Any integer is also a whole number. Choose only one answer below. a. True b. False False Correct. This statement is false. An integer can be negative, such as the number −100-100. −100-100 is not a whole number
Read all the options before answering. −17-17 is… Choose only one answer below. a. an integer b. a rational number c. a real number d. all of the above d. all of the above Correct. The answer is d. −17-17 is an integer, and all integers are also rational numbers, which in turn are real numbers.
According to the strictest definition, 0.070.07 is… Choose only one answer below. a. a whole number b. an integer c. a rational number d. a real number a rational number Correct. The answer is c. 0.070.07 is a decimal that ends and therefore a rational number because it can be written as a fraction.
π is… Choose only one answer below. a. a whole number b. an integer c. a rational number d. a real number a real number Correct. The answer is d. π is a real number whose complete decimal expansion goes on forever and does not repeat.
According to the strictest definition, −1/3 is… Choose only one answer below. a. an integer b. a rational number c. a real number d. All of the above a rational number Correct. The answer is b. According to the strictest definition, −1/3 is a rational number because it can be represented as a fraction.
-30,000 is… Choose only one answer below. a. greater than −45,000 b. less than −31,000 c. greater than 0 d. less than −50,000 a. greater than −45,000
Correct. The answer is a. −45,000 lies to the left of −30,000- on the numbers line and therefore is less than −30,000
Which answer shows the following numbers in order from least to greatest? a. −1/3, 2/3, 1/3, 5/3 b. 1/3, −1/3, 2/3, 5/3 c. −1/3 1/3, 2/3, 5/3 d. 5/3, 2/3, 1/3, −1/3 C
0, 1, 2 is a set of continuous data. True or False? Choose only one answer below. a. True b. False False Correct. This statement is false. 00, 11, and 22 are distinct consecutive integers. There are numbers, such as 1.51.5, between them, so they are not continuous.
Temperature is an example of continuous data. True or False? Choose only one answer below. a. True b. False True Correct. This statement is true. Temperature covers an entire interval of data and can be “measured” rather than counted, so it is continuous.
Timesheets log the days that a warehouse employees work each week. Does the week’s timesheet give data that is discrete or continuous? Choose only one answer below. a. Discrete. b. Continuous Discrete Correct. The answer is a. The days of the week are discrete and do not allow for values between them.
A graph shows the profit margin of a particular product at two different price points. Is this data discrete or continuous? Choose only one answer below. a. Discrete b. Continuous Discrete Correct. The answer is a. The graph shows discrete price points, not all possible prices, between two numbers.
A traffic monitor analyzes network usage and records upload and download speeds. Are these data discrete or continuous? Choose only one answer below. a. Discrete b. Continuous Continuous Correct. The answer is b. These are all continuous measurements for which it is possible to have fractional parts.
Which of the following is the correct translation of −3<y<4? Choose only one answer below. a. −3 is less than y� which is less than 4 b. −3 is less than or equal to y� which is less than or equal to 4 c. −3 is greater than y� which is greater than 4 d. −3 is less than y� which is less or than or equal to 4 −3 is less than y� which is less than 4 Correct. The answer is a. Both of the << symbols mean “less than,” so the correct translation is −3 is less than y� which is less than 4.
Which of the following is the correct translation of 10>x>6?
a. 10 is less than x� which is less than 6 b. 10 is less than or equal to x� which is greater than 6 c. 10 is greater than x� which is greater than 6 d. 10 is less than x� which is greater than 6 10 is greater than x� which is greater than 6
Correct. The answer is c. Both of the >> symbols mean “greater than,” so the correct translation is 10 is greater than x� which is greater than 6.
Which of the following is the correct translation of 8<z≤16?
a. z� is greater than or equal to 8, but less than or equal to 16 b. z� is greater than 8, but less than 16 c. z� is greater than 8, but less than or equal to 16 d. z� is greater than or equal to 8, but less than 16 c. z� is greater than 8, but less than or equal to 16
Correct. The answer is c. The < symbol means “less than” while the ≤ symbol means “less than or equal to,” so the correct translation is z� is greater than 8, but less than or equal to 16.
How would ” w is less than or equal to 9 , but greater than or equal to 5 ” be written?
a. 9≤w≤5 b. 9≥w≥5 c. 9≥w>5 d. 9≤w≥5 b. 9≥w≥5 Correct. The answer is b. Both ≥ symbols mean “greater than or equal to,” so 9≥w≥5 means ” w is less than or equal to 9 , but greater than or equal to 5 .”
How would ” x is greater than or equal to −4 , and less than 7 ” be written? Choose only one answer below. a. −4≥x≥7 b. −4≤x≤7 c. −4≤x<7 d. −4≥x>7 c. −4≤x<7 Correct. The answer is c. The signs are read “less than” giving the complete answer −4 is less than or equal to x and x is less than 7.
. Which of the following is an example of the identity property of addition? Choose only one answer below. a. 3+(−3)=0 b. (3+5)+2=3+(5+2) c. 54+16=16+54 d. 3+0=3 3+0=3 Click here to select this answer Correct. The answer is d. Adding zero to a number does not change its value.
7−3+12−1 Choose only one answer below. a. 21 b. 16 c. 15 d. −9 c. 15 Click here to select this answer Correct. The answer is c. 7−3=4 4+12=16 16−1=15
A box contains 100 pairs of gloves. There is a box on each of the two floors of a chemical testing and analysis company. The first floor uses 78 pairs per week and the second uses 56. Which expression shows how many gloves will be left by the end of the week? Choose only one answer below. a. 100−78+56 b. 100−78−56 c. 100+2−78−56 d. 100+100−78−56 d. 100+100−78−56
Which expression below is an accurate simplification of −3−(−4)+6−(2) ? Choose only one answer below. a. −3+4+6−2 b. −3−4+6−2 c. 3+4+6+2 d. −3−4+6+2 a. −3+4+6−2
True or False? A real number is divided by 0. The quotient is 0. Choose only one answer below. a. True b. False b. False Correct. This statement is false. A real number divided by 0 is undefined.
True or False? A real number multiplied by 0 is 0. Choose only one answer below. a. True b. False a. True Correct. This statement is true. Any real number multiplied by 0=0.
(−3)4 is equivalent to which of the following?
a. 3×3×3×3 b. −3×−3×−3×−3 c. 4×4×4 d. −4×−4×−4 b. −3×−3×−3×−3 Correct. The answer is b. (−3)4 tells you to multiply −3 by itself 4 times.
If a six-sided die is rolled 3 times, how many possible outcomes are there?
a. 6 b. 18 c. 36 d. 216 d. 216 Correct. The answer is d. Each roll has 6 possible outcomes, so 3 rolls have 63 or 216 possible outcomes.
If a couple has three children, how many different ways are there to order a series of boys and girls (assuming that birth order matters)?
a. 3^2 b. 3^3 c. 2^3 d. 2^2 c. 2^3
Correct. The answer is c. For each child, there are two possibilities, and there are 3 children. So the number of ways to have 3 children is 2×2×2=8 . (Here they are: BBB, BGB, BBG, BGG, GBB, GGB, GGG, GBG.)
Lindsey has 8 pairs of shoes. Every day, Monday through Friday, Lindsey chooses a pair of shoes at random. How many possible combinations of pairs of shoes could Lindsey wear to work this week? 8^5
A 66-sided die is rolled 55 times. How many possible combinations of outcomes are there after the 55 rolls? 6^5
This expression reads “six raised to the twelfth.” 6^12
Joe has 55 shirts, 55 jackets, 55 hats, and 55 pairs of pants. How many different outfit combinations does Joe have all together? 5^4
True or False? In the expression 3+5×7, the 5×7 operation should be done first according to PEMDAS. a. True b. False a. True Correct. This statement is true. Multiplication and division must be done before addition and subtraction.
True or False? In the expression 5+(5⋅5)3, the multiplication should be done within the parentheses before evaluating the exponent. Choose only one answer below. a. True b. False True Correct. This statement is true. Evaluating what is inside the parentheses first changes the expression to 5+(25)3. The problem asks us to multiply 25 by tself 3 times, not 5 by itself 3 times.
Which operation should be performed first in the following expression: 5+62−16÷4 Choose only one answer below. a. Addition b. Exponent c. Subtraction d. Division Exponent Correct. The answer is b. Because there are no parentheses in this expression, the exponents should be evaluated first.
Which operation should be performed first in the following expression: 32−92÷(1+2)
Choose only one answer below. a. Subtraction b. Exponent c. Division d. Addition Addition Correct. The answer is d. Whatever operations are inside the parentheses need to be performed first.
There are 81 people coming to a conference. How many different ways can the chairs for these people be arranged into rows with an equal number of chairs in each row? Reset
A. 5 B. 4 C. 3 D. 2 a Correct. The chairs can be arranged as 1 row of 81 chairs, 3 rows of 27, 9 rows of 9, 27 rows of 3, or 81 rows of 1 for a total of 5 different ways.
True or False? Two composite numbers can have exactly the same factors. Choose only one answer below. a. True b. False b. False Correct. This statement is false. Every composite number has a unique factorization.
True or False? A prime number has only itself as a factor. Choose only one answer below. a. True b. False b. False Correct. This statement is false. 11 is also a factor of every number, prime or composite.
What kind of number is 51? Choose only one answer below. a. Prime b. Composite Composite Correct. 3×17=51, so 51 is a composite number.
What kind of number is 27? Choose only one answer below. a. Prime b. Composite . Composite Correct. The answer is b. 27 is a composite number because it has the factors 1,3,9,27
What kind of number is 47? Choose only one answer below. a. Prime b. Composite Prime Correct. The answer is a. 47 is a prime number because it has no factors other than 1 and itself.
What is the prime factorization of 8 ? Choose only one answer below. a. 2⋅2 b. 2⋅2⋅2 c. 2⋅2⋅3 2⋅2⋅2 Click here to select this answer Correct. The answer is b. The prime factorization of 8 is 2⋅2⋅2 .
What is the prime factorization of 21 ?
a. 7⋅3 b. 7⋅2⋅3 c. 2⋅2⋅3⋅3 7⋅3 Click here to select this answer Correct. The answer is a. The prime factorization of 21 is 7⋅3 .
What is the greatest common factor of 1818 and 4545? Choose only one answer below. a. 33 b. 55 c. 99 d. 18 c. 9 Click here to select this answer Correct.The answer is c. 9 is the largest number that divides both 18 and 45 .
If a positive number squared is 36 , what is that number?
a. 3 b. 4 c. 5 d. 6 6
The integer 169 has
a. a principal square root of −13 b. a negative square root of −13 c. a negative square root of 13 d. no roots a negative square root of −13 Click here to select this answer Correct. The answer is b. Since −13 multiplied by itself is 169 it is a square root of 169. Since it is negative, it is referred to as the negative square root.
Every positive whole number has two square roots. True or false? Choose only one answer below. a. True b. False True Correct. This is a true statement. Every whole number has both a principal and a negative square root.
The radical sign refers to the negative square root of a real number. True or false? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The radical sign refers to the principal square root.
Which of each of the following would you use to classify 16−−√16? Prime or Composite? Odd or Even? Rational or Irrational? Composite, even, and rational
Fill in the blank with the correct equality or inequality symbol: -8 _ 6 < and ≠ would both work here
Which of the following statements is true? 8>8 8<8 8≥8 8≠8 Only 8≥8≥8 is true. 8≥8≥8 states that 8 is equal to or greater than 8.
An infinite, repeating decimal is considered an irrational number. True or False FALSE
In the expression (2−3)4, the first operation should be Subtract 3 from 2
The fact that the sum of a number and 00 will always equal the number is called The identity property
The product of two negative numbers will always equal a(n) _ number. POSITIVE
14−21+(−3) a −10 b −4 c 4 d 10 The correct answer is a. 14−21+(−3)
=−7+(−3)
=−10
A runner runs 14.5 miles, 12.25 miles, 21.75 miles, and 20.8 miles. What is an accurate estimate for the total number of miles? a 65
b 67
c 70
d 74 c) 70
8+(6−3)^2 a 14 b 17 c 31 d 35 b) 17
4^2−8+10 a 10 b 18 c 26 d 34 b) 18
Select the true statement from the following: a 0.15 is between 0.138 and 0.149 . b 0.22 is between 0.23 and 0.24 . c 0.34 is between 0.335 and 0.35 . d 0.46 is between 0.465 and 0.468 . c) 0.34 is between 0.335 and 0.35 .
−36÷3 a −13 b −12 c 12 d 13 b) −12
Which set of data is discrete? a Speed of a car b Weight of a dog c Adults in a household d Time to go to bed c) Adults in a household
4.4… is a(an) a integer. b only a real number. c rational number. d whole number. rational number. The correct answer is c. 4.44… is a repeating decimal and a rational number because it can be written as a fraction.
10^3 a 10 b 30 c 300 d 1000 d) 1000
A coin is flipped 4 times. How many different outcomes are there? a 8
b 16
c 32
d 64 b) 16
Which number is a prime number? a 21
b 22
c 23
d 24 c) 23
−5000 is a greater than −3000 . b greater than 0 . c less than −7000 . d less than 0 . d) less than 0.
What is the greatest common factor of 60 and 80 ? a 10
b 20
c 30
d 40 b) 20
Display x less than or equal to 4 using interval notation. a (−∞,4)
b (−∞,4]
c (4,∞)
d [4,∞) b) (−∞,4]
What is the prime factorization of 36 ? a 2×3
b 2×2×3
c 2×3×3
d 2×2×3×3 d) 2×2×3×3
What are all of the positive factors of 72 ? a 1,2,4,18,36,72
b 1,2,4,8,12,18,24,36,72
c 1,2,3,4,6,8,9,12,18,24,36,72
d 1,2,3,4,6,8,9,12,18,24,32,36,48,72 c) 1,2,3,4,6,8,9,12,18,24,36,72
Cori is in charge of ordering tablecloths for two dining rooms of the inn that she manages. The first dining room has 37 tables, and the second dining room has 41. Each tablecloth is generally changed twice a day. What is a good estimate of the total number of tablecloths she will need each day? a 35×2
b (35+35)×2
c (35+40)×2
d (40+40)×2 d) (40+40)×2
Which set of numbers is continuous? a integer b rational c real d whole c) real
Select the true statement from the following: a −4.5 is between −4 and −5 . b −3.8 is between −3 and −2 . c −2.3 is between −2 and −1 . d −1.2 is between −1 and 0 . a) −4.5-4.5 is between −4-4 and −5-5.
Display x is greater than −5 using interval notation. a (−∞,−5) b (−∞,−5] c (−5,∞) d [−5,∞) c) (−5,∞)
Which number is a composite number? a 71
b 73
c 77
d 79 c) 77
√3 is a(an) a) integer. b) only a real number. c) rational number. d) whole number B ONLY A REAL NUMBER The correct answer is b. 3-√3 is only a real number. Its complete decimal expansion goes on forever without repeating.
−32÷8=? a) −4 b) 24 c) 4 d) 40 -4
3^5÷9=? a) 252 b) 27 c) 9 d) 234 27
Which of the following is equal to 12 ? 3⋅4 −2⋅6 8⋅3 2⋅−6 −1⋅−12 −2⋅−10
a) A, B, C, and E b) B and E c) A and E d) A only A&e
What number system does −2 belong to? whole numbers integers rational numbers real numbers a) A and B b) B and D c) A, C, and D d) B, C, and D d) B, C, and D Correct. The correct answer is d. −2 is an integer (because it does not contain a fractional or decimal component), a rational number (since it can be written as a fraction), and a real number (because it can be placed on a number line).
√2 cannot be written as a fraction, but it can be placed on a number line. √2 is: a) a whole number b) an integer c) a rational number d) a real number REAL NUMBER
What is the prime factorization of 48 ? a) 2⋅2⋅2⋅2
b) 2⋅2⋅2⋅2⋅3
c) 2⋅2⋅2⋅2⋅3⋅3
d) 2⋅2⋅2⋅3⋅3 b) 2⋅2⋅2⋅2⋅3 Correct. The correct answer is b. 48=4⋅12 . Since 4 is the product of 2⋅2 and 12 is the product of 3⋅4 , the prime factorization of 48 therefore is 2⋅2⋅2⋅2⋅3
The GCF of two different prime numbers can only be 1. True or False?
a) True
b) False
TRUE
Display −3 is less than or equal to x , and 5 is greater than x using interval notation. a) (−3,5) b) [−3,5) c) (−3,5] d) [−3,5] b) [−3,5) Correct. The correct answer is b. All values greater than or equal to −3 and less than 5 are true for the inequality. Therefore, [−3,5) is the interval notation
During a three-day air show, there were 17,351 people on Friday, 24,718 people on Saturday, and 33,512 people on Sunday. What was the estimate attendance for the weekend? a) 74,000 b) 76,000 c) 78,000 d) 80,000 b) 76,000
Which set of numbers contains a prime number? a) 4,6,8 b) 7,9,15 c) 10,15,20 d) 14,21,28 7,9,157,9,15
Correct. The correct answer is b. 77 has only factors of 11 and 77, and so the set 7,9,157,9,15 contains a prime number.
What improper fraction is equivalent to the mixed number 7 1/4 ? Choose only one answer below. a. 28/4 b. 5/7 c. 29/4 d. 8/4 c. 29/4
Correct. The answer is c. 7⋅4=28 , and 28 added to the numerator 1 is 29. Therefore, 7 1/4 is equal to 29/4.
What mixed number is equivalent to the improper fraction 71/8 ?
a. 8 7/8 b. 7 7/8 c. 8 1/7 d. 8 1/8 8 7/8
What fraction with a denominator of 64 is equivalent to 5/16 ? Choose only one answer below. a. 5/64 b. 20/64 c. 4/64 d. 69/84 b. 20/64
What fraction with a denominator of 84 is equivalent to 9/14 ? Choose only one answer below. a. 14/84 b. 84/84 c. 9/84 d. 54/84 d. 54/84
An inch is 1/36 of a yard. How many inches are in 1/2 of a yard? 18
What fraction with a denominator of 100 is equivalent to 7/50 ? 14/100
Identify the common prime factor for the numerator and denominator: 4/6 ? 2
Identify the common prime factor for the numerator and denominator: 22/55 11
Which of the following statements are true regarding reducing fractions? Choose only one answer below. a. Reducing fractions requires canceling common factors. b. Mathematical operations are easier to perform when fractions are simplified. c. When fraction’s numerator and denominator have no common factors, it is considered to be simplified to its lowest terms. d. All of the above d. All of the above Correct. The answer is d. All of the above statements are true with regard to reduced fractions.
Which of the following is the reduced form of −8/64 ?
a. − 1/8 b. −1/8 c. 1/−8 d. All of the above d. All of the above
True or False? If a fraction contains two different prime numbers in both the numerator and denominator, it can be assumed that fraction is already reduced to its lowest terms. Choose only one answer below. a. True b. False true
Are the fractions 15/21 and 105/147 equal? yes 2205
Are the fractions 187/75 and 17/7 equal? no 1309 1275
You are given the fractions 7/x and y/92 , and you know that x⋅y=644 . Are these fractions equal? yes 7*9=644
You are given the fractions x/43 and 4/y , and you know that x⋅y=100 . Are these fractions equal? no 43*4=172
Which of the following is a multiple of 2 : 3 , 5 , 21 , or 86 86
Which of the following is a multiple of 3 : 1 , 5 , 15 , or 20 15
6 and 14 . Least common multiple 42
12 and 8 . Least common multiple 24
What multiple of 6 is closest to 62 ? 60
What multiple of 7 is closest to −40 ? -42
What is the LCM of 9 and 6 ? Choose only one answer below. a. 9 b. 12 c. 18 d. 54 c. 18
What is the LCM of 14 and 28 ? Choose only one answer below. a. 14 b. 28 c. 196 d. 392 b. 28
For the numbers 7 and 9 , is the common multiple 63 also the least common multiple? Choose only one answer below. a. Yes, it is also the least common multiple. b. no Yes, it is also the least common multiple.
8/9 and 5/6 LCD 18
3/4 and 5/7 LCD 28
12/25 and 3/50 LCD 50
5/14 and 3/10 LCD = 70
What is 3/4 of 2/5 3/10
4/9÷1/6 2 2/3
1÷3/5 1 2/3
6/11÷−5 /12 -1 17/55
Which digit is in the hundredths place in the following number: 8,653.237
Choose only one answer below. a. 3 b. 2 c. 8 d. 7 3
Which digit is in the ten-thousandths place in the following number: 180,921.80467
Choose only one answer below. a. 8 Click here to select this answer b. 4 Click here to select this answer c. 6 Click here to select this answer d. 0 6
True or False? The number 8.0049 has greater value than 8.0050 . Choose only one answer below. a. True b. False false
This statement is false. Notice that the first number has a 44 in the thousandths place whereas the second number has a 55. Just as 40004000 is less than 50005000, 44 thousandths is less than 55 hundredths. The 99 and 00 at the ten-thousandths place are irrelevant since that place is less than the thousandths place, so while 0.0009>0.00000.0009>0.0000, 8.0049<8.00508.0049<8.0050. Therefore, the first number does not have the greater value.
Round 76.358 to the nearest ten 80
Round 76.358 to the nearest tenth. 76.4
Round 25,432.9816 to the nearest thousand. 25000
Round 472.4348 to the nearest hundredth. 472.43
Round 25,432.9816 to the nearest thousandth. 25432.982
Round 99.97 to the nearest tenths. 100
Round 1,317.5 to the nearest tens 1320
Round 189.73 to the nearest ones. 190
True or False? When rounding the number 12,000.859 to the nearest tenths, the tenths digit will be increased by 1 . Choose only one answer below. a. True b. False true
How much is −27.0918 rounded to the nearest hundredths? Choose only one answer below. a. −27.10 Click here to select this answer b. −27.09 Click here to select this answer c. 27.08 d. 27 -27.09
How much is 5,000 rounded to the nearest ten thousands? Choose only one answer below. a. 10,000 Click here to select this answer b. 0 Click here to select this answer c. 5,000 Click here to select this answer d. 1,000 10000
The number 142,010.37589 was rounded to 142,010.376. To which place value was the number rounded? Choose only one answer below. a. Nearest tens b. Nearest tenths c. Nearest hundredths d. Nearest thousandths d. Nearest thousandths
True or False? 2.22 will become 2.220 when evaluating the following expression:20.002+2.22= ? Choose only one answer below. a. True b. False true
True or False? When dividing decimals by hand using long division, it is necessary to convert the divisor to a whole number. Choose only one answer below. a. True b. False true
True or False? Like addition and subtraction, when multiplying decimals it is also necessary to add trailing zeros. Choose only one answer below. a. True b. False false
80.7024÷5.52= ? Choose only one answer below. a. 12.702452 Click here to select this answer b. 14.62 Click here to select this answer c. 14.527 Click here to select this answer d. 13.85 14.62
True or False? A percent is a part of a whole. That whole is always equal to 100100. Choose only one answer below. a. True b. False true
True or False? To find the decimal equivalent of a percentage, you simply move the decimal point two places to the right. Choose only one answer below. a. True b. False false
27.2%+3% 30.2%
99.9%−54.371%−45.529% 0%
−37.4×31.5% -11.781
300÷150% 200
Which of the following decimal numbers is equal to: 8.23%
Choose only one answer below. a. 0.823 Click here to select this answer b. 82.3 Click here to select this answer c. 0.0823 Click here to select this answer d. 0.00823 .0823
625% 6.25
True or False? The question “what is x� percent of y� amount?” requires multiplication. Choose only one answer below. a. True b. False true
20/16=x/4 Solve for the variable x 5
72/x=450/50 Solve the following for the variable x : 8
300/200=120/z Solve the following for the variable z : 80
. 20% of 80 16
What percent of 65 is 32 ? (round your answer to the nearest tenth. 49.2 Correct. Set up the percent proportion to solve. x/100=32/65 . Cross multiply (65/x)=(100×32) . 65x=3200 Solve for x by dividing each side by 65 . x=49.2%
True or False? A ratio is a comparison that expresses for every x amount you have of quantity A; you have y amount of quantity B. Choose only one answer below. a. True b. False a. True Correct. This statement is true. A ratio is a way to express a comparison between two quantities.
True or False? A percent proportion is always set up to express the percentage value over 100 . Choose only one answer below. a. True b. False . True Correct. This is a true statement. To set up the percent proportion, you express the percentage over 100 .
Which of the following is a method of cross-multiplication ? Choose only one answer below. a. The linear method b. The ratio method c. The butterfly method d. The conditional method c. The butterfly method Correct. The answer is c. The butterfly method is a cross-multiplication method used to determine whether two fractions are equal. The numerator of one fraction is multiplied by the denominator of the opposite fraction on both sides.
True or False? When solving a conditional proportion problem, the first step is to determine which part of the fraction (numerator or denominator) has the unknown values, and then work that part of the fraction. Choose only one answer below. a. True b. False False
Correct. This is a false statement. The first step in solving a conditional proportion problem is to determine which part of the fraction (the numerator or denominator), has the unknown values, and then work with the other part of the fraction, the one with 2 known values.
True or False? Ratios that are unequal are proportional. Choose only one answer below. a. True b. False b. False Correct. This is a false statement. Two ratios are proportional only if they are equivalent.
Convert 20/100 to a decimal number. .2
Convert 3 7/20 to a decimal number 3.35
Convert 7.12 to a mixed number 7 3/25
Convert −12.3 to a mixed number -12 3/10
4.90×0.78= ? a 3.1902 b 3.822 c 4.263 d 3.553 3.822
79.6%−45.8%= ? a 24.80%
b 33.80%
c 31.10%
d 28.40% 33.80%
How many Tablespoons (Tbsp.) are in 1 cup (c.) of liquid? a 8
b 16
c 24
d 32 16
14/25 a 28% b 56% c 70% d 84% 56%
If the cost of a product is $50 per 5 cubic feet (cu. ft) of volume, what is the cost of the product per cubic foot? a $5 to 1 cubic foot (cu. ft)
b $10 to 1 cubic foot (cu. ft)
c $1 to 2 cubic foot (cu. ft)
d $50 to 1 cubic foot (cu. ft) b $10 to 1 cubic foot (cu. ft)
What is the least common multiple of 6 and 12 ? a 6
b 12
c 18
d 24 b 12
Convert 50° F to degrees in Celsius. a 10°
b 17.77°
c 27.78°
d 122° 10°
How many cups (c.) are in 1 L of fluid? (Round your answer to the nearest tenth) a) 4.2 c. b) 4.3 c. c) 4.6 c. d) 4.7 c. 4.2
How many ounces (oz.) are in .5 kg? Round your answer to the nearest tenth. a) 17.2 oz. b) 17.6 oz. c) 18.1 oz. d) 18.3 oz. 17.6
Which of the following operations are elementary operations? Only addition and subtraction Only multiplication and division Only addition and multiplication Addition, subtraction, multiplication, and division Addition, subtraction, multiplication, and division
What elementary operation will you use to generate the value 7 from the constants 3 and 4? Addition Subtraction Multiplication Division Addition
What elementary operation will you use to generate the value 9 from the constants 3 and 3? Addition Subtraction Multiplication Division Multiplication
Which of the below are constants? Select the most correct answer. 3.23.2 3737 −0.0009-0.0009 All of the above All of the above
Which of the following is a constant? −0.000016 x 3y 2w −0.000016
In the expression 3^2×5÷1−2 , which value is a base? 3
2
5
1 3
Which of the following contains an elementary operation? 16−−√
4+5
16
0.0000003 4+5
Which of the following is an arithmetic expression? x=y
x
5
2+18 2+18
What is 5 called in 12^5 ? a base an exponent an expression a variable 5 is an exponent 12 is base
True or False? All constants are rational numbers. Choose only one answer below. a. True b. False false
The following string of numbers and operations is an arithmetic expression. True or False? 10−5÷2×8+36
Choose only one answer below. a. True b. False true
You know that the variable x represents the value of 5 , and the variable y represents the value of 3 . Evaluate x+y . Choose only one answer below. a. 2 Click here to select this answer b. 5 Click here to select this answer c. 8 Click here to select this answer d. 15 8
You know that the variable a represents the value of −2 , and the variable b represents the value of 7 . Evaluate a⋅b . Choose only one answer below. a. −14 Click here to select this answer b. −5 Click here to select this answer c. 3 Click here to select this answer d. 9 -14
The following expression contains variables. True or false? 10−5÷2×8+36
Choose only one answer below. a. True b. False . False Correct. This is a false statement. The expression above does not contain an unknown symbol or letter which is a variable.
4a is equal to… Choose only one answer below. a. 4+a Click here to select this answer b. 4−a Click here to select this answer c. 4⋅a Click here to select this answer d. 4÷a c. 4⋅a
How many terms are in the following expression: 3b−4c
Choose only one answer below. a. 1 Click here to select this answer b. 2 Click here to select this answer c. 3 Click here to select this answer d. 4 b. 22 Click here to select this answer Correct. The answer is b. The terms in the expression are 3b and 4c. A term can also be any number of constants and variables multiplied together. Here, subtraction separates the two terms from one another.
When writing an algebraic expression, it is best to write the constants at the end of the expression. True or False? Choose only one answer below. a. True b. False True Correct. This is a true statement. When writing an algebraic expression, it is best to write the constants at the end of the expression.
Identify the terms of the following expression: 1+465f2g6+29f3g2
Choose only one answer below. a. There are 3 terms: 1 , 465f2g6 , and 29f3g2 Click here to select this answer b. There are 3 terms: 1+465 , f2g6 , and f3g2 Click here to select this answer c. There are 2 terms: 1 , and 465f2g6+29f3g2 Click here to select this answer d. There are 2 terms 3
You need to write an expression that adds together the terms 8X2 , 2Y4, 3XY3, and 27 . What is the correct order for the terms to show in the final expression? Choose only one answer below. a. 8X2+2Y4+3XY3+27 Click here to select this answer b. 8X2+3XY3+2Y4+27 Click here to select this answer c. 27+2Y4+3XY3+8X2 Click here to select this answer d. 2Y4+3XY3+8X2+27 2Y4+3XY3+8X2+27 Click here to select this answer Correct. The answer is d. 2Y4+3XY3+8X2+27 . Always write expressions in descending order of exponent value with constants at the end of the expression. In the given terms, the term 2Y4 has the largest exponent, so it is written first, with lower exponents following in order. The constant 27 comes last. Therefore, the answer is 2Y4+3XY3+8X2+27 .
In the term 4xy^3 , 4 is a… Choose only one answer below. a. coefficient b. exponent c. operation a. coefficient
The 2 in 4x^2 indicates… Choose only one answer below. a. that the quantity of x is doubled. Click here to select this answer b. that the quantity of x is multiplied by itself Click here to select this answer c. that there are 4 x ‘s in the expression Click here to select this answer d. that the x ‘s should be added together b. that the quantity of x is multiplied by itself
Correct. The answer is b. The 2 in 4x^2 means that the x is multiplied by itself.
When writing an algebraic expression, it is best to write the constants at the end of the expression. True or False? Choose only one answer below. a. True b. False true
Which of the following correctly matches each operation with its inverse? Choose only one answer below. a. Subtraction → multiplication Addition → subtraction Division → addition Multiplication → division b. Subtraction → multiplication Addition → division Division → subtraction Multiplication → addition c. Subtraction → addition Addition → division Division → multiplication Multiplication → subtraction d. Subtraction → addition Addition → subtraction Division → multiplication Multiplication → division d. Subtraction → addition Addition → subtraction Division → multiplication Multiplication → division
The process for undoing multiplication and division operations will always work, even if one of the numbers is zero. True or False? Choose only one answer below. a. True b. False false
A number y is divided by 2,456 . What operation should be performed to yield a value of y ? Choose only one answer below. a. 2,456 should be added to the quotient. Click here to select this answer b. 2,456 should be subtracted from the quotient. Click here to select this answer c. 2,456 should be multiplied by y . Click here to select this answer d. the quotient should be multiplied by 2,456 . d. the quotient should be multiplied by 2,456 . Click here to select this answer Correct. The answer is d. Since y was divided by 2,456 , in order to get y again, the quotient should be multiplied by 2,456 . (y2456)×2456=y
Two operations are considered inverse operations if they undo one another. True or False? Choose only one answer below. a. True b. False true
It is most desirable to leave a mathematical expression the way it is given to you. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. It is most desirable to shorten the expression by combining all the terms that can be combined.
Are there any like terms in the following expression? 4c+3j+2z−9m ? Choose only one answer below. a. Yes b. No No Correct. The answer is b. All of the variables are different, so there are no like terms to combine.
After like terms are combined in the following expression, what will it read? 3r−13y+5m−2r
Choose only one answer below. a. rm−13y Click here to select this answer b. −5r−13y+5m Click here to select this answer c. −13y+5m Click here to select this answer d. r−13y+5m r−13y+5m Click here to select this answer Correct. The answer is d. 3r−2r=1r, which should be written as r.
After combining terms what would 2x+3x−7+4h−x look like? Choose only one answer below. a. 8−x Click here to select this answer b. 4x+4h−7 Click here to select this answer c. 5x−7+4h−x Click here to select this answer d. 5x−4h−x 4x+4h−7 Click here to select this answer Correct. The answer is b. 2x+3x−x=4x . It does not matter whether the 4h or 4x is placed first. The answer is 4x+4h−7 .
You are given the term 9C7 . A like term to this term would have the same variable, but what should this like term have for the exponent? Choose only one answer below. a. −9 Click here to select this answer b. 3 Click here to select this answer c. 7 Click here to select this answer d. 9 7
Which of the below is a like term with 45g^2h^4
Choose only one answer below. a. h^4 Click here to select this answer b. g^2 Click here to select this answer c. 24gh^2 Click here to select this answer d. −6g^2h^4 −6g^2h^4
Which of the below is an unlike term with V^2W^2 ? Choose only one answer below. a. V^2W^2 Click here to select this answer b. V^3W Click here to select this answer c. −V^2W^2 Click here to select this answer d. 0.3V^2W^2 b. V^3W
The constant 4 is equivalent to the constant 4 multiplied by a variable with an exponent of 0 . True or False? Choose only one answer below. a. True b. False True Correct. This is a true statement. Since a variable with an exponent of 0 is equivalent to 1, a constant can be imagined as having an implied variable with an exponent of 0, e.g., 4=4^0 .
What is the classification of the following expression? U^2+V^2+W^2
Choose only one answer below. a. Constant b. Linear c. Quadratic d. Cubic c. Quadratic
Simplify the following expression using the distributive property: K(a+b+c)
Choose only one answer below. a. Kabc b. Ka+Kb+Kc c. a+b+c d. Ka+b+c b. Ka+Kb+Kc
Simplify the following expression using the distributive property: d−(2e+20)−4
Choose only one answer below. a. d+2e+20 Click here to select this answer b. d−2e+16 Click here to select this answer c. d−2e−24 Click here to select this answer d. 2e+20d−4 d−2e−24 Click here to select this answer Correct. The answer is c. Imagine an invisible 1 outside the parentheses, then distribute it to the terms inside the parentheses, and simplify by combining like terms. Therefore, d−(2e+20)−4=
d−1(2e+20)−4=
d−2e−20−4=
d−2e−24 .
Simplify the following expression using the distributive property: P(3−Q)−3(P+Q)
Choose only one answer below. a. 6P−2PQ Click here to select this answer b. −PQ−3Q Click here to select this answer c. PQ−3P+Q Click here to select this answer d. 3−Q−3P−3Q b. −PQ−3Q Click here to select this answer Correct. The answer is b. There are two instances in which distributive property can be applied: P(3−Q) and −3(P+Q) . Distribute each separate instance individually and then proceed to simplify the expression. For −3(P+Q) , remember that if an expression inside a set of parentheses is being multiplied by a negative number, you need to apply that negative sign to the entire encased expression. So:P(3−Q)−3(P+Q)=3P−PQ−3P−3Q . Now simplify by combining like terms. Therefore 3P−PQ−3P−3Q=−PQ−3Q .
Simplify the following expression by combining like terms: D(D^2+D)+D^2
Choose only one answer below. a. D3+2D2 Click here to select this answer b. 3D2+D Click here to select this answer c. D3+2D Click here to select this answer d. D3+D2+D a. D^3+2D^2
Simplify the following expression using the distributive property: e(0.4e+0.6e)+e^2
Choose only one answer below. a. e+e^3 Click here to select this answer b. 0.4e2+0.6e^2 Click here to select this answer c. e+e^2 Click here to select this answer d. 2e^2 2e^2
Simplify the following expression using the distributive property: fg−g(f−g−8)−g^2
Choose only one answer below. a. 2fg Click here to select this answer b. g−8−g2 Click here to select this answer c. −fg−8−g2 Click here to select this answer d. 8g fg−fg+g^2+8g−g^2=8g
What part of the expression below is important for determining the expression’s degree? 3x^4+7w+62
Choose only one answer below. a. 3 Click here to select this answer b. 4 Click here to select this answer c. x Click here to select this answer d. 62 4
What is the constant in the expression below? 5/x^2+15x−3.4
Choose only one answer below. a. 5 Click here to select this answer b. 2 Click here to select this answer c. 15 Click here to select this answer d. −3.4 d. −3.4 Click here to select this answer Correct. The answer is d. The constant is the value at the end of an algebraic expression. It is not part of a product with any variables.
Which of the following below is NOT an equation? Choose only one answer below. a. 45=y Click here to select this answer b. w3⋅Q=uQ+5v Click here to select this answer c. 45y4−13y3+10y+4 Click here to select this answer d. 7×2+4x+3=15 c. 45y4−13y3+10y+4 Click here to select this answer Correct. The answer is c. Because there is no equals sign, this is a mathematical expression, rather than a mathematical equation.
An equation of degree 1 is called a linear equation. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. A linear equation has a variable with a degree of 1 .
Which of the following demonstrates the principle of equality? Choose only one answer below. a. x+4=3y−16 x+4=3y−12 Click here to select this answer b. 4x−17=7w 4x=7w−17 Click here to select this answer c. 9m+6=c+10 9m+6−6=c+10−6 Click here to select this answer d. 19m+9=43r+3 19m=43r+3+9 c. 9m+6=c+10 9m+6−6=c+10−6 Correct. The answer is c. Since 6 was subtracted from the left, it needs to be subtracted from the right side.
What needs to be done to the left side of the equation based on what happened to the right side of the equation below? 8(m−n)=7c−19y+34
8(m−n) _ =7c−19y+4
Choose only one answer below. a. 4 should be subtracted from it. Click here to select this answer b. 4 should be added to it. Click here to select this answer c. 30 should be subtracted from it. Click here to select this answer d. 30 should be added to it. c. 30 should be subtracted from it.
Which equation is equivalent to the equation below? (w3)⋅Q=uQ+5v+20
Choose only one answer below. a. (w3)⋅Q−25=uQ+5v+5 Click here to select this answer b. (w3)⋅Q=uQ+5v Click here to select this answer c. (w3)⋅Q−20=uQ+5v Click here to select this answer d. (w3)⋅Q+15=uQ+5v+15 c. (w3)⋅Q−20=uQ+5v Click here to select this answer Correct. The answer is c. Since the constant on the right side of the equation went from +20 to 0, 20 was subtracted from the right. So 20 was also subtracted from the left. This shows the principle of equality.
The principle of equality states that if a number is added to one side of the equation, it should be subtracted from the other side. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. If a number is added to one side of the equation, it should be added to the other side as well.
Solve the following equation for t . 3t−7−2t=16÷2
Choose only one answer below. a. t=−1 Click here to select this answer b. t=7 Click here to select this answer c. t=8 Click here to select this answer d. t=15 d. t=15
Solve the following equation for y . 1.5⋅12−y=9+22÷11
Choose only one answer below. a. −8 Click here to select this answer b. 7 Click here to select this answer c. 11 Click here to select this answer d. 15 b. 7
Solve the following equation for x . (21−3)÷(−3+9)=x+9
Choose only one answer below. a. −15 Click here to select this answer b. −9 Click here to select this answer c. −6 Click here to select this answer d. 12 c. −6
Solve the following equation for U . U⋅(−2+5)÷(4−7)=0.5
Choose only one answer below. a. −6 Click here to select this answer b. −3 Click here to select this answer c. −1 Click here to select this answer d. −0.5 d. −0.5
You have the equation 9x+43=95−4x . Someone told you that the solution of this equation is x=−4. Using substitution, can you confirm that the solution is correct? Choose only one answer below. a. Yes, the solution is correct. b. No, the solution is incorrect. No, the solution is incorrect. Correct. The answer is b. When using substitution, we substitute a variable with its known value and evaluate. To check if the provided solution x=−4 is correct, we substitute x with −4 everywhere x appears, and evaluate. So the equation becomes 9(−4)+43=95−4(−4), and evaluating both sides results in −36+43=95+16, or 7=111. Both sides are not equal, therefore the solution must be incorrect.
Solve the following equation for g . 24g−5=g+10
Choose only one answer below. a. −1 Click here to select this answer b. 1 Click here to select this answer c. 15 Click here to select this answer d. 16 1
Solve the following equation for M . M÷(7.5−7)=52
Choose only one answer below. a. −25 Click here to select this answer b. 2.5 Click here to select this answer c. 12.5 Click here to select this answer d. 50 12.5
Solve the following equation for y . y+2y+3y=4y+5
Choose only one answer below. a. −1 Click here to select this answer b. 1.25 Click here to select this answer c. 2.5 Click here to select this answer d. 3.5 2.5
Solve the following equation for a. 3^2(1−a)=−6a
Choose only one answer below. a. −9 Click here to select this answer b. 0 Click here to select this answer c. 2 Click here to select this answer d. 3 3
You need to solve the following equation for a, given that b=3 . Which math principle will you apply first? ab=4b^2
Choose only one answer below. a. Combining like terms b. Distribution c. Substitution d. Subtraction principle of equality c. Substitution Correct. The answer is c. To simplify the equation, you will first want to replace all appearances of b with an actual value. Therefore, the first math principle you will apply is substitution.
Solve the following equation for Q , given that u=3 and v=2 . (uv)⋅Q+v=uQ+vu
Choose only one answer below. a. Q=6 Click here to select this answer b. Q=−1 Click here to select this answer c. Q=2 Click here to select this answer d. Q=1 d. Q=1
Solve the following equation for N , given that M=4 . M(N+1)=3N+4
Choose only one answer below. a. N=−3 Click here to select this answer b. N=−1 Click here to select this answer c. N=0 Click here to select this answer d. N=2 c. N=0
Solve the following equation for w . w/2+w/2=4−w
Choose only one answer below. a. w=−1 Click here to select this answer b. w=0 Click here to select this answer c. w=1 Click here to select this answer d. w=2 d. w=2
Solve the following equation for g , given that h=4 and k=3. (hg−kg)÷9=g+8
Choose only one answer below. a. g=−9 Click here to select this answer b. g=−8 Click here to select this answer c. g=7 Click here to select this answer d. g=17 a. g=−9
Which of the following points lies on the x -axis? Choose only one answer below. a. (0,−7) Click here to select this answer b. (1,1) Click here to select this answer c. (−7,0) Click here to select this answer d. (0,3) c. (−7,0)
If all of the points were graphed on a coordinate plane, which of the points below would be at the top? Choose only one answer below. a. (0,18) Click here to select this answer b. (−23,−45) Click here to select this answer c. (22,5) Click here to select this answer d. (45,−45) a. (0,18)
The point (0,0)(0,0) is called the original. True or false? Choose only one answer below. a. True a. False a. False Correct. This statement is false. The point (0,0)(0,0) is called the origin.
What is the slope of the following linear equation: y=−98x+16 -98
What is the y-intercept of the following linear equation: y=−39x+96 96
Write the following equation in slope-intercept form: −9x+y−1=0 y=9x+1
What is the slope of the following linear equation: −4x+2y−10=0 2
What is the y -intercept of the following linear equation: y=24x−88 Choose only one answer below. a. y Click here to select this answer b. 24 Click here to select this answer c. −88 Click here to select this answer d. 88 c. −88
What is the slope of the following linear equation: y=−16x+29
Choose only one answer below. a. −29 Click here to select this answer b. 29 Click here to select this answer c. −16 Click here to select this answer d. x c. −16
The following is written in slope-intercept form. True or false? y−4=2(x−1)
Choose only one answer below. a. True a. False a. False Correct. This statement is false. Slope-intercept form is y=mx+b .
Put the equation below into slope-intercept form. 2x/4−1/4=3y
Choose only one answer below. a. y=1/6x−1/12 Click here to select this answer b. y=1/6x−1 Click here to select this answer c. y=1/3x−1/3 Click here to select this answer d. y=1/3x−1 a. y=1/6x−1/12
What are the slope and one point in the line whose equation is given below? y+4=3x−12
Choose only one answer below. a. Slope 3 , (4,−12) Click here to select this answer b. Slope 3 , (−4,4) Click here to select this answer c. Slope 3 , (4,−4) Click here to select this answer d. Slope −3 , (12,4) Slope 3 , (4,−4) Click here to select this answer Correct. The answer is c. In slope-intercept form, the equation is y=3x−16. So the slope is 3. Using trial and error, we see that substituting 4 in for x and −4 in for y yields −4=3(4)−16=−4, a true equation. So, (4,−4) is a point on the line.
If the rise =5 and the run =1 , what is the slope of the line? 5
Using the formula rise over run, what is the rise of a line that has the following two coordinates: (0,0) and (3,6) ? 6
Using the formula rise over run, what is the run of a line that has the following two coordinates: (0,0) and (3,6) ? 3
Using the formula rise over run, what is the rise of a line that has the following two coordinates: (2,2) and (7,−13) ? -15
Using the formula rise over run, what is the run of a line that has the following two coordinates: (2,2) and (7,−13 )? 5
A line has the coordinates of (2,5) and (3,−5) . Will the slope go uphill or downhill? downhill
Find the slope of a line that passes through the coordinates (2,1) and (6,3) . Choose only one answer below. a. 1/2 b. 2 c.1/5 d. 1/3 1/2
What is the rise of a line that contains the coordinates (x1,y1)=(0.2,0.5) and (x2,y2)=(0.9,0.1)? Choose only one answer below. a. 0.4 Click here to select this answer b. −0.4 Click here to select this answer c. 0.7 Click here to select this answer d. −0.7 b. −0.4
Which statement is true of the run? Choose only one answer below. a. In the rise over run formula, it is the denominator. b. It is calculated using the x -values of any two coordinates in a line. c. It can be positive, negative, smaller than the rise, larger than the rise, or the same number as the rise. d. All of the above d. All of the above Correct. The answer is d. Each of these statements is true of the run.
What is the slope of the following linear equation: 6x+2y+12=0
Choose only one answer below. a. −12 Click here to select this answer b. −6 Click here to select this answer c. −3 Click here to select this answer d. 8 c. −3
What is the y-intercept of the following linear equation: y=−5(−3x+6)+7 Choose only one answer below. a. 7 Click here to select this answer b. −30 Click here to select this answer c. 15 Click here to select this answer d. −23 d. −23
What is the y -intercept of the following linear equation: 12x=10−2y Choose only one answer below. a. 5 Click here to select this answer b. 10 Click here to select this answer c. −2 Click here to select this answer d. −5 a. 5
A line has a slope of −3 and passes through the point (5,2) . What is the equation of the line in slope-intercept form? Choose only one answer below. a. y=5x+2 Click here to select this answer b. y=−3x+2 Click here to select this answer c. y=−3x+17 Click here to select this answer d. y=2x−3 c. y=−3x+17
A line has a slope of −6 and passes through the point (−1,−4) . What is the y -intercept of the line? Choose only one answer below. a. −10 Click here to select this answer b. −6 Click here to select this answer c. −5 Click here to select this answer d. −24 a. −10
Simplify the inequality: (Enter your answer with the x variable on the left) −3x−8>x x<-2
A solid line in the graph of an inequality indicates that the value of y can be equal to the values on the line. True or false? Choose only one answer below. a. True b. False . True Correct. A solid line indicates that the inequality used was ≤ or ≥ . In both cases, the y values on the line are included.
In the inequality y>2x+5 , when x=−3 , y can equal which of the following values? (There is more than one correct answer). Choose only one answer below. a. −0.999 Click here to select this answer b. −1 Click here to select this answer c. −1.0001 Click here to select this answer d. 1 a. −0.999
The following inequality would have solutions in which quadrants? y≥2x+7
a. I only b. I and II only c. I, II, and III only d. I, II, III, IV c. I, II, and III only
In the inequality y≤−1.5x+4 , when x=−3 , y can equal ANY of which set of numbers? Choose only one answer below. a. −8.5 , −1 , 0 , 7 , 10 Click here to select this answer b. −10 , −8.5 , 0 , 3 , 9 Click here to select this answer c. 0 , 5 , 17 , 27 Click here to select this answer d. −9 , −1 , 0 , 7 , 8.5 d. −9, −1, 0, 7, 8.5
Correct. When x=−3 , the inequality simplifies to y≤−1.5(−3)+4 , so y≤8.5 . All those numbers are less than or equal to 8.5 .
. Each section of a pie chart corresponds to a category of data. True or False? Choose only one answer below. a. True b. False true
When creating a pie chart, the percentages for each category are calculated from the data. True or False? Choose only one answer below. a. True b. False true
The sum of all the percents in a pie chart add up to 100%100% or close to it because of rounding. True or False? Choose only one answer below. a. True b. False true
The height of each bar in a bar chart is determined by the number of values in the category for that bar. True or false? Choose only one answer below. a. True b. False true
When constructing a bar chart, it is not necessary to include all of the data collected. True or false? Choose only one answer below. a. True b. False false
In a dot plot, depending on the data collected, every data value or groups of data values can be represented by a dot. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. In a dot plot, each data value is represented as a point, or dot, on the graph.
The first step in building a dot plot is to draw a horizontal scale. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. In order to determine the scale of the horizontal axis, we need to know what the maximum and minimum values are, so the first step should be arranging the data in increasing order.
You are constructing a stem plot. The value of one of your data points is 8282. The stem for this data point would be 88, leaf would be 22. True or false? Choose only one answer below. a. True b. False True Correct. This is a true statement. A stem plot is constructed by separating each data value into a stem (usually the left-most digit) and a leaf (usually the right-most digit).
Numerical summaries that describe measures of central tendency of a data set include the mode, the median, and the mean. True or False? Choose only one answer below. a. True b. False true
The mean, median, and mode can each be the same for a data set. True or False? Choose only one answer below. a. True b. False true
The mean, median, and mode can each be different for a data set. True or false? Choose only one answer below. a. True b. False true
There can be more than one mean for a set of data. True or false? Choose only one answer below. a. True b. False false
Outliers do not often affect the mean measure of center. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. Outliers can heavily affect the mean in a distribution. When a distribution is skewed, the mean value will see a direct impact.
Which measure of center applies best to skewed distribution? Choose only one answer below. a. Median b. Mean c. Standard deviation a. Median Correct. The answer is a. Because the mean can be largely affected by extreme values on either side of a distribution, median is the most appropriate measure of center for a skewed distribution.
The data set below includes the ages of those working in an office. Make a Stemplot for the following data and identify which value in the data set may be an outlier? Choose only one answer below. a. 1919 Click here to select this answer b. 3838 Click here to select this answer c. 6666 Click here to select this answer d. None of the above a. 1919
Click here to select this answer
Correct. The answer is a. While 1919 is a possible outlier (since there is a gap in the stem plot), it is worth checking this with the 1.5 IQR1.5 IQR criterion. Doing this shows that it is not actually an outlier.
The average of the smallest two numbers in a data set of seven numbers is the first quartile. True or false? Choose only one answer below. a. True b. False b. False Correct. This statement is false. In a data set of seven numbers, the second number is the value at the first quartile, not the average of the first two numbers.
True or False? The standard deviation for data points above the mean is different from data points below the mean. Choose only one answer below. a. True b. False False Correct. This is a false statement. There is one standard deviation for a data set. You might think of it as the average distance of all the data points from the mean, both above and below.
According to the IT support group at your company, during any given week employees need anywhere from 4 to 40 loaner laptops as a result of technical issues with their computers. Based on this data the range of loaner laptops required is 36 . What do you think the standard deviation is? Choose only one answer below. a. Larger than 36 Click here to select this answer b. 36 Click here to select this answer c. Smaller than 36 Click here to select this answer d. Less than 0 c. Smaller than 36 Click here to select this answer Correct. The answer is c. The standard deviation cannot be larger than 36 because the standard deviation has to be smaller than the range. The standard deviation cannot be the same, because only if all the data points have the same value can the standard deviation and range be the same. The standard deviation cannot be less than 0 because standard deviation is never negative. Therefore, for this set of data, the standard of deviation must be less than 36 .
Your boss has asked you to upgrade the loaner laptops with newer models. Having analyzed the data from IT on the need for loaner laptops, you want to be sure you have enough laptops for worst-case scenarios. What statistic from the IT data will you use as a guide? Choose only one answer below. a. Mean b. Minimum c. Range d. Standard Deviation e. Maximum e. Maximum Correct. The answer is e. Mean, minimum, and standard deviation are incorrect as you are concerned with “worst-case scenarios.” Range is not correct as it is influenced by the minimum. Therefore, maximum is correct in determining if you will have enough laptops for “worst-case scenarios” as it will provide a benchmark for the most loaner laptops needed during a given week.
Find the first quartile ( Q1 ) for the following data set: {73, 80, 77, 8, 39, 90, 63, 18, 66} a) 28.5 b) 50 c) 66 d) 78.5 a) 28.5 Correct. The correct answer is a. Q1 is the median of the “lower half” of the data set. Here, Q1 falls midway between 18 and 39, which is 28.5.
Find the interquartile range ( IQR ) of the following data set: {1, 1, 7, 8, 17, 18, 21, 27, 42, 45, 45, 46, 46, 54, 57, 78} a) 12.5 b) 33.5 c) 34.5 d) 46 33.5
Find the third quartile ( Q3 ) for the following data set: {13, 19, 71, 71, 76, 53, 22, 64, 56, 61, 24} a) 22 b) 49 c) 56 d) 71 71
Which of the following most accurately describes a quartile?
a) The difference between Q3Q3 and Q1Q1.
b) Four equally sized groups of numbers within a set.
c) Values that provide a cut-off between four equally sized groups of numbers within a set.
d) There are four in a set: the minimum, the mean, the median, and the maximum.
c) Values that provide a cut-off between four equally sized groups of numbers within a set.
Identify the five-number summary for the following data set: {2, 8, 13, 14, 16, 18, 18, 23, 42, 46} a) 2,8,17,42,46 b) 2,13,17,23,46 c) 2,13,18,23,46 d) 2,13,20,23,46 b) 2,13,17,23,46 Correct. The correct answer is b. The minimum of the data-set is 2 , the first quartile is 13 , the median is 17 , the third quartile is 23 , and the maximum is 46 .
Find the second quartile ( Q2 ) for the following data set: {1, 3, 4, 12, 17, 22, 99, 31, 34, 41, 71, 72, 99} a) 8 b) 22 c) 31 d) 71.5 c) 31 Correct. The correct answer is c. Q2, also known as the median, is the midpoint of the data set. Here, that value is 31
Find the first quartile ( Q1 ) for the following data set: {2, 15, 16, 16, 18, 22, 24, 38, 45} a) 15.5 b) 16 c) 18 d) 31 15.5
Find the third quartile ( Q3 ) for the following data set: {1, 3, 7, 19, 20, 29, 34, 37} a) 5 b) 19.5 c) 26.5 d) 31.5 31.5
Find the interquartile range ( IQR ) of the following data set: {1, 7, 17, 24, 39, 40, 42, 46, 49} a) 12 b) 32 c) 39 d) 44 b) 32 Correct. The correct answer is b. IQR=Q3−Q1=44−12=32
What is the interquartile range? a) The difference between the third quartile and the first quartile. b) The difference between the maximum and the minimum. c) A list of the values within a quartile. d) The five numbers that are represented on a box plot. a) The difference between the third quartile and the first quartile.
Mode is a measurement not often affected by outliers. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. Mode measures the most frequent value in a data set. A significant outlier would not necessarily affect the mode of a data set.
Find the mean of the following data set: 69, 2, 7, 10, 28, 21, 16, 40, 86 a) 21 b) 31 c) 44 d) 86 b) 31 Correct. The correct answer is b. (69+2+7+10+28+21+16+40+86)÷9=279279÷9=31
There is a set of data containing five numbers. You order these five numbers from least to greatest. The middle number (the third largest and third smallest) is 54 . 23, 36, 54, 58, 65 What does the number 54 represent in this data set? a) Mean b) Median c) Mode d) Standard Deviation b) Median
Correct. The correct answer is b. The median is the midpoint of a data set, when ordered from least to greatest.
What is the mode of a set of data values? a) The largest value in a data set b) The midpoint of a data set c) The value that appears most frequently in a data set d) The difference between the largest and smallest value in a data set c) The value that appears most frequently in a data set
Correct. The correct answer is c. The mode is the most frequent value in a data set.
Find the range of the following data set: 29, 31, 4, 24, 14, 61 a) 19 b) 27 c) 57 d) 61 c) 57 Correct. The correct answer is c. 61−4=57 .
You are examining a set of data. The mean of the data set is 32 . The data is normally distributed. Approximately 68% of all values fall between 23 and 41 . Approximately 95% of all values fall between 14 and 50. What is the best estimate for the standard deviation of this data set? a) 9 b) 18 c) 23 d) 41 a) 9 Correct. The correct answer is a. Following the empirical rule, we know that approximately 68% of all values are within one standard deviation of the mean, and approximately 95% of all values are within two standard deviations of the mean.
Find the maximum of the following set of values: 71, 36, 89, 85, 89, 54, 42, 99, 65, 67 a) 36 b) 63 c) 89 d) 99 99
Which of the following represent the five values included in the five-number summary of a data set? Choose only one answer below. a. minimum, first quartile, mean, third quartile, maximum b. minimum, first quartile, median, third quartile, maximum c. minimum, mode, mean, median, maximum d. first quartile, mode, mean, median, third quartile b. minimum, first quartile, median, third quartile, maximum Correct.
A 3-year longitudinal study was conducted to investigate the approval ratings for the mayor of New City among registered voters. In 2014 among 86,748 registered voters surveyed, 58,593 gave the mayor a favorable rating. In 2015 among 82,523 registered voters surveyed, 52,931 gave the mayor a favorable rating. In 2016 among 84,169 registered voters surveyed, 55,475 gave the mayor a favorable rating.
What type of variable is in this study? Categorical Quantitative Cannot be determined Categorical
What type of chart(s) would be best to display this data? A bar chart A stem plot Either a or b None of the Above A bar chart
A study was conducted on the number of attendees each day at the state fair. You are asked to recommend a method for displaying the data graphically so that the shape of the data can be seen, and each data value is also visible. What would be the best choice among the following? (Enter the letter that corresponds with your choice.) a. Bar chart b. Histogram c. Scatterplot d. Stem plotplot d. Stem plot The answer is d. Stem plot is the best choice as these types of graphs show the shape of a data set and each data value.
You are designing a study of the number of hours worked by financial analysts working at a particular firm. You are especially interested in knowing if there are any outliers in the data, as well as the median number of hours worked and the approximate distribution of the data. Which graphical display would satisfy your needs? a. Bar chart b. Histogram c. Stem plot d. Box plot The answer is d. A box plot is a good display to use to show the shape of a data set, as well as outliers (if any).
A senior executive at a financial firm sent out a one-question survey to the 1,505 fund managers at her firm asking “Are you able to exercise each of these principles in the course of your daily responsibilities?” The five principles were listed, and respondents had to indicate a “Yes/No” for each. The executive is planning to display this data in a histogram. Is this the appropriate graph choice? a. Yes b. No The answer is b. No, a histogram is not the correct choice. It is used for continuous (quantitative) data and this data is categorical.
In a study on the root causes of order fulfillment processing errors, the authors included the following data, from interviews, on the cause of mistakes. The most common causes were interruptions during order picking (21% ), being short staffed ( 12% ), being subject to time constraints ( 11% ), employee fatigue ( 9.4% ) and look alike/sound alike products ( 8.5% ). Norman, a senior warehouse manager building a presentation on order fulfillment processing errors, wanted to convey this data to his shipping department. What display should he use? a. Pie chart b. Histogram c. Stem plot d. Box plot The answer is a. A pie chart is a good display in this case. The data is categorical and there are not too many categories.
A marketing researcher was investigating residential water usage in a metropolitan area for a report she was putting together for a client. She polled individual households and asked them to report their average monthly water bill. The lowest average monthly water bill was $35.17 and the highest average monthly water bill was $153.20 . When presenting the data, she did not want the decimal values to get lost. What display would you suggest she use? a. Histogram b. Pie Chart c. Stem plot d. Box Plot The answer is c. A stem plot is a good choice as you can see the distribution of the data and the values are preserved.
To better understand their student’s lifestyles and study habits, the dean at a local college checked the GPA of students referred to the academic advising center for tutoring. If their GPA was 2.5 or lower, she asked students to estimate how many hours they typically spend studying per day. What display should she use to share her data with colleagues? a. Bar Chart b. Pie Chart c. Data Table d. Histogram The answer is d. Histogram is correct as the data is quantitative.
The graph chosen to display data can affect how the data is interpreted. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. Data that can be displayed using different graphs may be interpreted in different ways.
To avoid misrepresentation in a pie chart, all sections need to be similar sizes. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. To avoid misrepresentation in a pie chart, sections should be labeled and include the percentages they represent.
You are a professional trainer at a local sports academy. You ask your athletes to determine the number of grams of protein they consume for a particular meal. Which of the following would be the best choice to illustrate the shape of the data you collect? a Bar chart b Pie chart c Box plot d None of the above c Box plot
Feedback: The correct answer is c. As the data you are collecting is quantitative data, from the choices below a box plot would be your best choice to illustrate the shape of the data.
What is the most significant difference between histograms and bar charts? a The number of bars used b The use of labels on the axes c The type of data depicted in the graph d The coloring used for each bar Feedback: The correct answer is c. A bar chart measures categorical data. A histogram displays quantitative data.
Arrange the mean, median, and mode in order from least to greatest in a distribution that it is positively skewed. a Median, mode, mean b Mean, median, mode c Mean, mode, median d Mode, median, mean Mode, median, mean
Feedback: The correct answer is d. The median will always remain in the middle for skewed data, and the mean goes towards the skew. The mode goes in the opposite direction of the skew.
The bitrate of audio files in a sample group of files ranged from 160 kilobytes per second (Kbps) to 256 kilobytes per second (Kbps). What percentage of the audio files will fall within 2 standard deviations of the mean? Assume the data is normally distributed. a 34%
b 68%
c 95%
d 99.7% Feedback: The correct answer is c. The Standard Deviation Rule says that 95%95% of the values will fall within 22 standard deviations of the mean.
Determine any outliers in the following data set. {1,24,26,28,32,36,38,40,65}
a 1 b 65 c A and B d None Feedback: The correct answer is c. Q1=25Q1=25, Q3=39Q3=39. IQR=Q3−Q1=14IQR=Q3-Q1=14.
Using the 1.5 IQR Criterion Rule, outliers would be less than Q1−1.5 IQR=25−1.5(14)=4, or greater than Q3+1.5 IQR=39+1.5(14)=60.
Since 1 is less than 4 and since 65 is more than 60, these two values (1 and 65) are outliers by definition.
The return on investment (ROI) in a sample population of investments ranged from 8% to 23% . What percentage of the sample will fall within 1 standard deviation above the mean? Assume the data is normally distributed. a 47.5% b 13.5% c 68% d 34% Feedback: The correct answer is d. The Standard Deviation Rule says that 68% of the values will fall within 11 standard deviation of the mean. Since we are looking for the percentage that will fall 1 standard deviation above the mean, we divide this value in half. Therefore, the answer is 34%.
Which of the four different sets of numbers would have the greatest standard deviation? a 5,5,5,5,5
b 5,6,7,8,9
c 1,8,16,25,33
d 40,43,45,47 Feedback: The correct answer is c. Ordering the data set yields the following:
Stem plots display which type of data? a Quantitative b Categorical c Neither Quantitative nor categorical d Quantitative and categorical Feedback: The correct answer is a. Stem plots display quantitative data.
It is important to start the frequency scale on a bar chart at which value to be certain not to overemphasize a difference in values? a Zero b The lowest measured value c The smallest frequency d As long as the scale is even, it doesn’t matter where you start it. Feedback: The correct answer is a. A vertical scale that does not start at zero can exaggerate the differences in a data set.
Which of the following are best used to display categorical data? a Histogram b Dot plot c Pie chart d Stem plot Feedback: The correct answer is c. A pie chart is used to display categorical data. All of the other choices are used to display quantitative data.
Determine Q3 for the sorted list of data values. {3,8,8,10,16,20,20,23,27,37,44,45,62,71}
a 27
b 37
c 44
d 45 Feedback: The correct answer is c. There are 14 data points so Q2 falls between 20 and 23 . The upper half of the data includes the following 7 data points: 23,27,37,44,45,62,71 . Therefore, Q3=44 .
Determine the range for the following data set. {1,24,26,28,32,36,38,40,65} a 1 to 65
b 64
c 65 64
Determine the median for the following set of diagnostic test scores. {60,47,65,85,81,77,70,56,47,84,75}
a 67
b 70
c 47
d 67.9 70
Of the following sets of data, which would you assume should have the greatest range? a Age when a baby gets their first tooth b Age of first-year business students c Age of death d Age of high school graduate c age of death
When observing a box plot, what percentage of the measured data lies between Q1Q1 and the maximum value in the list? a75% b50% c25% 75%
Determine the interquartile range ( IQR ) for the following set of diagnostic test scores. {60,47,65,85,81,77,70,56,47,84,75}
a 25
b 57
c 68
d 80 Feedback: The correct answer is a. IQR=Q3−Q1IQR=Q3-Q1. {47,47,56,60,65,70,75,77,81,84,85}{47,47,56,60,65,70,75,77,81,84,85}. Q1=56Q1=56. Q3=81Q3=81. IQR=81−56=25IQR=81-56=25.
When analyzing a possible relationship for two-variable data, if both variables are categorical, what is the most appropriate choice to display the data? Side-by-side boxplots Scatterplot Bar chart Two-way frequency table Histogram Two-way frequency table
When working with two-variable data, if the explanatory variable is categorical and the response variable is quantitative, what is the most appropriate choice to display the data? Side-by-side boxplots Scatterplot Bar chart Two-way frequency table Histogram Side-by-side boxplots
When working with two-variable data, if both variables are quantitative, what is the most appropriate choice to display the data? Side-by-side boxplots Scatterplot Bar chart Two-way frequency table Histogram Scatterplot
What does ” C→C ” refer to? a) Both the explanatory and response variables are categorical. b) There is a causal relationship between the two variables. c) There is a correlation between the explanatory and response variables. d) There are two categorical, explanatory variables. a) Both the explanatory and response variables are categorical.
Which graphical display is most appropriate when the explanatory variable is categorical and the response variable is quantitative?
a) Two-way table
b) Scatterplot
c) Contingency table
d) Side-by-side box plot
d) Side-by-side box plot
A business was analyzing the effectiveness of two different marketing campaigns (Campaign A and Campaign B) that were developed to promote the same product. The business was interested in determining which campaign appealed more to a specific customer segment – males aged 18 to 24 . The marketing department asked 500 males from this age category which ad campaign they preferred and would most influence them to purchase the product. Which of the following labels best fits the explanatory and response variables? a) The explanatory variable is “Customer Preference,” and the response variable is “Marketing Campaign Type.” b) The explanatory variable is “Marketing Campaign A,” and the response variable is “Customer Segment.” c) The explanatory variable is “Customer Segment,” and the response variable is “Customer Preference.” d) The explanatory variable is “Marketing Campaign Type,” and the response variable is “Customer Preference.” d) The explanatory variable is “Marketing Campaign Type,” and the response variable is “Customer Preference.”
Continuing with the previous example, from Question 3 , which of the following graphical displays should be used? a) Horizontal side-by-side box plot b) Scatterplot c) Vertical side-by-side box plot d) Two-way table d) Two-way table
In a two-way table, which best describes the sum of all of the joint frequencies?
a) The total number of individuals in the study.
b) The marginal frequency.
c) The correlation coefficient (r�).
d) The total number of individuals in the treatment group.
a) The total number of individuals in the study.
A side-by-side box plot:
a) is always horizontal.
b) is always vertical.
c) can be either horizontal or vertical.
d) whether it is horizontal or vertical depends upon whether there is a positive or negative correlation.
c) can be either horizontal or vertical.
When both variables are quantitative, how is a scatterplot created?
a) The points are plotted on a coordinate plane based on their ordered pairs.
b) A line is drawn connecting all of the points to one another.
c) A box is drawn from the first quartile to the third quartile, with a line in the middle at the median.
d) A table is created, where each cell counts the frequency of the corresponding row and column occurring.
a) The points are plotted on a coordinate plane based on their ordered pairs.
Correct. The correct answer is a. When both variables are quantitative, a scatterplot created by plotting the points on a coordinate plane based on their ordered pairs.
What does ” C→Q ” refer to? a) There is a correlation between the categorical variable and the quantitative variable. b) The explanatory variable is categorical, and the response variable is quantitative. c) One variable is categorical, and the other variable is qualitative. d) There is a correlation between the quantitative variables. b) The explanatory variable is categorical, and the response variable is quantitative.
Correct. The correct answer is b. The notation “C→Q�→�” means the explanatory variable is categorical and the response variable is quantitative.
Which graphical display is most appropriate when both variables are quantitative?
a) Horizontal side-by-side box plot
b) Two-way table
c) Scatterplot
d) Vertical side-by-side box plot
c) Scatterplot
Correct. The correct answer is c. If both variables are quantitative, a scatterplot is usually the best choice to display their relationship.
A marketing company is conducting a study examining the relationship between average monthly spending (in dollars) and the monthly amount spent on eating out at restaurants (measured in dollars). Which of the following labels best fits the explanatory and response variables?
a) The explanatory variable is “average monthly spending on eating out at restaurants,” and the response variable is “monthly spending.”
b) The explanatory variable is “average monthly spending,” and the response variable is “monthly amount spent on eating out at restaurants.”
c) The explanatory variable is “average spending,” and the response variable is “monthly spending.”
d) The explanatory variable is “average spending on food,” and the response variable is “monthly spending.”
b) The explanatory variable is “average monthly spending,” and the response variable is “monthly amount spent on eating out at restaurants.”
Continuing with the previous example, from Question 44, which of the following graphical displays should be used?
a) Side-by-side plot
b) Two-way table
c) Scatterplot
d) Contingency table
c) Scatterplot
Correct. The correct answer is c. A scatterplot is the appropriate graphical display when both variables are quantitative.
In a two-way table, what does the sum of the joint frequencies in one row equal?
a) The quantitative variable.
b) A marginal frequency.
c) The correlation coefficient r�.
d) The number of individuals in the placebo group.
b) A marginal frequency.
When can two-way tables be used?
a) When both the explanatory and response variables are quantitative.
b) When both the explanatory and response variables are categorical.
c) When one variable is categorical and the other variable is quantitative.
d) Two-way tables are used regardless of whether the variables are categorical or quantitative.
b) When both the explanatory and response variables are categorical.Correct. The correct answer is B. Two-way tables are used when both the explanatory and response variables are categorical.
A scatterplot is useful for which type of data? a. Both variables are categorical. b. One variable is categorical, one variable is quantitative. c. Both variables are quantitative. d. One variable is discrete, one variable is continuous. c. Both variables are quantitative.
True or False? A scatterplot always shows the explanatory variable on the horizontal, or x-axis. a. True b. False true
The strength of the correlation between two variables can be measured by which statistic? a. Relationship factor b. Correlation coefficient ( r ) c. Strength test d. Trending statistic b. Correlation coefficient ( r )
A company is studying the effectiveness of two different production processes (Process A and Process B) for a week. The results are measured by counting the number of products without defects and with defects. Which numerical measure could be used to analyze the data? Choose only one answer below. a. Correlation coefficient ( r ) Click here to select this answer b. Five-number summary c. Median d. Conditional percentages d. Conditional percentages Correct. The answer is d. Both variables are categorical (C→C) so we will use a two-way table. Therefore, our numerical measure will be conditional percentages.
The company also wants to measure the time each process takes. The company measured the time it took to make each product as it came off of the assembly line. Which numerical measure would present the maximum and minimum amount of time that it took for products to be made using each process system? Choose only one answer below. a. Relative Frequency b. Five-number Summary c. Correlation d. Conditional percentages b. Five-number Summary Correct. The answer is b. In this study one variable is categorical, and the other is quantitative (C→Q) . The five-number summary will show five important statistical values: minimum, maximum, first quartile, median, and third quartile. Therefore, the five-number summary would be the best choice to look at the minimum and maximum values for both processes.
Amarketer was interested in how age affects responses to images of healthy food. He sampled a population ranging in age from 10 years old to 70 years old. Subjects were asked to complete a simple survey, rating how much they would like to eat the food shown in 10 images. The rating went from 1 (not at all) to 10 (very much). The food depicted was all food considered healthy. Which numerical measure could be used to analyze the strength of the relationship between age and response to images of healthy food? Choose only one answer below. a. Correlation coefficient ( r ) b. Conditional percentages c. Mean d. Five-number Summary a. Correlation coefficient (r) Click here to select this answer Correct. The answer is a. In this study both variables are quantitative (Q→Q) that form paired data. The strength of a correlation can be measured by calculating the correlation coefficient ( r ).
A car company is comparing the miles its trucks can go before needing repair to that of one of its rivals. The researchers want to compare the middle 50% of the data for both groups. Which numerical measure would identify the two values that 50% of the data falls between for both groups? Choose only one answer below. a. Median b. Five-number summary c. Mode d. Joint Frequencies b. Five-number summary Correct. The answer is b. In this study one variable is categorical and the other is quantitative (C→Q) . The five-number summary will show five important statistical values: minimum, maximum, first quartile, median, and third quartile. 50% of the data falls between the first( Q1 ) and third( Q3 ) quartile, so the researchers should look at the five-number summary to determine the values for Q1 and Q3 for both groups, as these values define the middle 50% of the data.
The presence of outliers have little effect on correlation. True or False? Choose only one answer below. a. True b. False false
The larger the sample size, the greater the effect an outlier will have on correlation. True or False? Choose only one answer below. a. True b. False false
CableNow, an Internet provider company, is conducting a customer satisfaction survey on TV cable installation services. The company sends an email to all customers with a link to the survey and an offer to receive a discount on the next month’s bill. What is the type of study design? Choose only one answer below. a. Observational b. Experimental c. Random sampling d. Stratified a. Observational Correct. The answer is a. This is an example of an observational study. The key property of an observational study is that the researcher is measuring or surveying the members of a sample without trying to affect them.
What type of sampling method is the company using? Choose only one answer below. a. Simple random b. Voluntary c. Stratified d. Cluster b. Voluntary
CableNow, an Internet and cable TV provider company, is conducting a customer satisfaction survey on TV cable installation services. The company sends an email to all customers with a link to the survey and an offer to receive a discount on the next month’s bill.Based on the information given, is there any potential bias in this study? Choose only one answer below. a. Yes, because the sampling frame does not match the intended population. b. Yes, because all customers were invited to participate in the study. c. No, because the sampling method will give a representative sample. d. No, because the sampling frame will match the intended population. a. Yes, because the sampling frame does not match the intended population. Correct. The answer is a. The company sent out a survey to all customers, including those who did NOT receive the service. Therefore, the sampling frame is not representative of the intended population — the customers who recently received installation services. The sampling method (voluntary) may also be a cause of bias because portions of the intended population may not be represented.
An association between two variables is a strong indication of causation. True or False? Choose only one answer below. a. True b. False b. False
Correct. This statement is false. An association between two variables is not a strong indication of causation. Often there are associations between two variables where causation does not exist.
Causation is a cause-and-effect relationship between two variables. True or False? Choose only one answer below. a. True b. False a. True Correct. This statement is true. Causation indicates a cause-and-effect relationship between two variables.
Sunscreen sales increase when shark attacks become more frequent, therefore there is a causal relationship. True or False? Choose only one answer below. a. True b. False b. False Correct. This statement is false. There is not a proven cause-and-effect relationship between sunscreen sales and shark attacks. This is an association, but a causal relationship does not exist.
The time value of money states that a “dollar today is worth more than a dollar tomorrow.” Economists have shown that inflation is the cause of the reduction in value of the dollar over time. Therefore, there is a causal relationship between inflation and the value of the dollar. True or False? Choose only one answer below. a. True b. False a. True Correct. This statement is true. There is a proven cause-and-effect relationship between inflation and the reduction in value of the dollar.
Productivity rates decrease as exposure to sunlight decreases. Therefore, there is a causal relationship between sunlight exposure and productivity. True or False? Choose only one answer below. a. True b. False b. False Correct. This statement is false. We have not shown a proven cause-and-effect relationship between lack of sunlight exposure and productivity. This is an association, but we cannot be sure that a causal relationship exists without more information.
A lurking variable is a variable that is included in an original study. True or False? false
Lurking variables are unimportant for a correct understanding of cause and effect. True or False? false
A lurking variable only affects the response variable. True or False? false
A lurking variable can hide the true relationship, or falsely identify a strong relationship, between variables. True or False? true
A study shows that there is a negative relationship between a student’s anxiety before a test and the student’s score on the test. Which is a possible lurking variable? Choose only one answer below. a. Student’s anxiety b. Student’s score c. Student’s time spent studying d. No lurking variable c. Student’s time spent studying Correct. A student’s time spent studying is a possible lurking variable. This variable was not included in the study, but could be associated with both variables.
A study shows that in the United States, there is a negative relationship between a person’s wealth and their likelihood of having student loan debt. Which of the following is a possible lurking variable? Choose only one answer below. a. Marital status b. Student loan status c. Gender d. Height in inches b. Student loan status Correct. Whether or not the individual applied for and accepted a student loan offer is a possible lurking variable. This variable was not included in the study, but could be associated with both variables.
An association can be explained by a lurking variable when a causal relationship is not present. True or False? Choose only one answer below. a. True b. False a. True Correct. An association does not necessarily indicate that causation exists. The presence of a lurking variable can often explain the association.
. If a trend appears in two groups and we combine the two groups’ data, the trend will always hold in the larger, combined group of data. True or False?
This statement is false. When Simpson’s Paradox occurs, a trend that appears in groups of data disappears once the groups are combined
Simpson’s Paradox can occur when the sizes of the groups are inconsistent. True or False? This statement is true. Simpson’s Paradox possibly could occur if the sizes of the groups are inconsistent.
Which of the following can prevent Simpson’s Paradox from occurring? Having the greatest number of people in the highest performing trial. Having the greatest number of people in the lowest performing trial. Having each person be exposed to each method in the trial. Having an equal number of people being exposed in the method groups in each trial. Having an equal number of people being exposed in the method groups in each trial.
What type of variable can cause a Simpson’s Paradox? Nominal variable Categorical variable Lurking variable Ordinal variable
How do wages depend on age or years of education?
response
How do stock prices depend on dividends and the company’s earnings reports?
response
How does a product’s sales depend on price?
explanatory
How do SAT scores depend on income?
explanatory
How does net profit margin depend on price?
explanatory
Complete the following sentence. Regression analysis is used to _____. calculate the probability that an event will occur. determine if there is an association between two or more variables. predict future values based on known values. determine a cause and effect relationship between two or more values. predict future values based on known values.
If unemployment levels are associated with inflation, economic recessions, and changes in technology, which of these is the response variable? Unemployment level Inflation Economic resources Changes in technology Unemployment level
If a salesperson’s commission, performance review, and raise are all dependent on sales volume, which of these is the explanatory variable? Commission Raise Performance review Sales volume Sales volume
Consider the following equation y=7x+15 . What is the slope of the line? 7
−7
7/15
−1/7 7
Consider the following equation, y=7x+15 . What is the y -intercept for this equation? 1
7/15
7
15 15
Suppose there is a linear equation y=1.5x+39 where x is the cost of production of a product and y is total cost. Which of the following is the correct interpretation of this slope? For every additional dollar of production costs there is a corresponding 39 dollar increase in total costs. For every additional dollar of production costs there is an additional 1.5 dollar increase in total costs. For every 1 dollar increase in total costs there is an additional 39 dollar increase in production costs. For every 39 additional dollars spent in production costs, there is an 1.5 dollar increase in total costs. For every additional dollar of production costs there is an additional 1.5 dollar increase in total costs.
Suppose there is a linear regression equation y=180−10x where x is equal to the number of users on a network and y is equal to network speed easured in Mbps. Which of the following is the correct interpretation of this slope? For every additional user on the network there is a corresponding 10 Mbps decrease in network speed. For every 10 Mbps reduction in network speed there is an additional 180 users on the network. For every 10 users on the network, there is a corresponding 1 Mbps increase in network speed. For every 180 users on the network, there is a corresponding 10 Mpbs increase in network speed. For every additional user on the network there is a corresponding 10 Mbps decrease in network speed.
A linear regression equation takes the following form: y=mx^2+b . True or False? False Correct. This statement is false. This is not the form that a linear regression equation takes. Linear regression is always of degree 1 , so the exponent of 2 associated with the x makes this a non-linear equation.
A linear regression “best-fit-line” can be estimated using least squares. True or False? Choose only one answer below. a. True b. False True Correct. This statement is true. Least squares estimation is the most common technique used to estimate the best-fit-line in linear regression.
Linear extrapolation is always a reliable method of prediction. True or False? Choose only one answer below. a. True b. False b. False Correct. This statement is false. Extrapolation assumes that the linear pattern of the data will continue outside of the range of data points. This may not always be the case and therefore may not always be a reliable method of prediction.
Linear interpolation is a technique used to make a prediction that falls between known data points. True or False? Choose only one answer below. a. True b. False . True Correct. This statement is true. Linear interpolation is a technique used to make a prediction that falls between known data points, using the linear regression equation.
Least squares estimation is a technique for predicting future data values. True or False? Choose only one answer below. a. True b. False b. False Correct. This statement is false. Least squares estimation is a technique used to estimate the best-fit-line in linear regression.
Extrapolation is always inappropriate. True or False? True False This statement is false. There are applications of extrapolation, and times in which it is necessary. Be mindful of the situation and try to avoid inappropriate extrapolation by considering the context.
Which of the following qualities of a sample help ensure the accuracy of any analysis, including a regression analysis? a large sample a representative sample Both a and b The answer is c. When conducting a study, it is important to use a large, representative sample.
Which of the following improves a study’s reliability as it increases? Correlation coefficient Regression equation slope Sample size Simpson’s Paradox The answer is c. Small study populations can impact the reliability of regression analysis. It is important to be aware of the sample size when attempting to perform a regression analysis or interpret data results based on small sample size.
Which of the following statements is most appropriate with regards to representative samples? The risk of non-representative sample decreases as sample size increases. The risk of non-representative sample decreases as sample size decreases. The risk of non-representative sample increases as sample size increases. The sample size has no bearing on whether or not the sample size is representative. The answer is a. In general, the risk of non-representative sample decreases as sample size increases.
What factor is most important to obtain a correct conclusion when performing regression analysis? Small sample size Large sample size Random missing data Variation in population The answer is b. The greater the sample size, the more likely you are to come to a correct conclusion.
Through what method can you identify if missing data is skewing the results of the study? Obtain basic statistics for the entire population and compare those with the sample being studied. Perform regression analysis for every subgroup of the sample being studied. Obtain a new sample of study subjects and compare the results with the original sample. Reduce the sample size to ensure less variation across the study population. The answer is a. While it is difficult to identify if missing data is skewing the results of the study, one approach is to obtain basic statistics for the entire population and compare those with the sample being studied.
In what form is a simple linear regression equation usually written? a) point-slope b) x=my+b c) slope-intercept d) a+b=y c) slope-intercept Correct. The correct answer is c. A simple linear regression equation is usually written in slope-intercept form.
Which of the following is true about simple linear regression? a) It can be used for any correlation, regardless of the degree of the relationship. b) Once the regression equation is found, any number of x can be plugged in to determine the expected y -value. c) It can be used to determine the relationship between two explanatory variables and one response variable. d) It is usually written in the form y=mx+b d) It is usually written in the form y=mx+b
Which of the following situations prevents an accurate regression analysis from being performed?
a) The relationship between the explanatory and response variable is linear.
b) The data you are looking for falls outside of the range of the study.
c) The sample size in the study is too large.
d) The association between the two variables is causal.
b) The data you are looking for falls outside of the range of the study.
Correct. The correct answer is b. If the data falls outside the range of the study, it is inappropriate to run a regression analysis on it.
A scatter plot shows the potential correlations and relationships between two variables. True or False? True False This statement is true. A scatterplot shows the potential correlation or relationship between the explanatory and response variable.
A strong correlation always explains a cause-and-effect relationship between two variables. True or False? True False This statement is false. A correlation does not prove that one variable causes another. It is possible that both of the variables in question are affected by some other factor, or that one variable is a subset of the other.
In addition to measuring linear relationships, the correlation coefficient can be used to measure curvilinear and parabolic relationships. True or False? True False This statement is false. The correlation coefficient measures if two variables have a linear relationship with one another.
Correlation coefficient is designated by which signs? Superscripts and subscripts Positive and negative signs Up and down arrows Decimal points The answer is b. The sign of the coefficient, which is either positive or negative, designates the relationship between two variables.
Which of the following correlation coefficients describes a strong, positive correlation? a) −0.9 b) −0.2 c) 0.2 d) 0.9 d) 0.9 Correct. The correct answer is d. A strong, positive correlation is represented by a correlation coefficient that is close to 1 , such as 0.9 .
What does a weak correlation look like on a scatterplot? a) The points follow closely along a line that moves down and to the right. b) The points do not follow very closely to a line. c) The points follow closely along a line that moves up and to the right. d) All of the above. The points do not follow very closely to a line. Correct. The correct answer is b. In a weak correlation, the points do not follow very closely to a line.
What best describes a scatterplot that has a correlation coefficient of 0 ? a) The points closely follow a line that is moving down and to the right. b) The points do not seem to follow any discernible linear pattern. c) The points closely follow a line that is moving up and to the right. d) The points loosely follow a line that is moving down and to the right. b) The points do not seem to follow any discernible linear pattern.
Correct. The correct answer is b. A correlation coefficient of 00 represents the weakest correlation. In fact, it indicates that there is no linear correlation. Therefore, it would be perfectly reasonable that the points do not seem to follow any discernible linear pattern.
What does a strong, positive correlation look like on a scatterplot? a) The points follow closely along a line that moves down and to the right. b) The points do not follow closely to a line. c) The points follow closely along a line that moves up and to the right. d) All of the above. c) The points follow closely along a line that moves up and to the right.
Correct. The correct answer is c. In a strong, positive correlation, the points follow very closely to a line that moves up and to the right.
3) What best describes a scatterplot that has a correlation coefficient of 1 ? a) The points closely follow a line that is moving down and to the right. b) The points do not seem to follow any discernible pattern. c) The points exactly follow a line that is moving up and to the right. d) The points loosely follow a line that is moving down and to the right. c) The points exactly follow a line that is moving up and to the right. Correct. The correct answer is c. A correlation coefficient of 1 indicates the strongest possible positive correlation, in fact it would be a perfectly linear set of points. Therefore, the points closely follow a line that is moving up and to the right, if there is a correlation coefficient of 1 .
A result is significant if it was likely caused by chance. True False The answer is b. This statement is false. A result is significant if it was unlikely to have been caused by chance.
A result is significant if the p -value is … less than the significance level greater than the significance level The answer is a. If the p-value is less than the significance level, the result is significant.
For a hypothesis test with a significance level of 0.05 , what p -value would be statistically significant? 0.02
0.06
0.08
0.1 The answer is a. A p-value less than the significance level is considered to be statistically significant. For a test with a significance level of 0.05, a p-value of 0.02 is statistically significant.
If a hypothesis test results in a p -value of 0.2 , what is the probability the result was caused by chance? 10%
20%
60%
80% The answer is b. A p-value of 0.2 means that there is a 20% probability the result was caused by chance.
Which of the following significance levels carries the lowest risk of accidentally drawing a conclusion when the result was actually caused by chance? 0.08
0.06
0.04
0.02 The answer is d. A significance level of 0.02 indicates that you only declare significance if there is less than a 2% chance that the result is caused by chance.
For a hypothesis test with a significance level of 0.1 , what p -value would not be statistically significant? 0.1
0.14
0.02
0.08 The answer is b. A p-value greater than the significance level is considered to be not statistically significant. For a test with a significance level of 0.1, a p-value of 0.14 is not statistically significant.
If a hypothesis test yields a result that 8% of the results occurred by chance, what is the p -value of this study? 0.02
0.2
0.08
0.8 The answer is c. If 8% of the results occurred by chance, the p -value for the study is 0.08.
If the significance level is set at .10 what p-value would be considered statistically significant? 0.08 0.12 0.14 0.16 The answer is a. If 10% of the result occur by chance, the significance level for the study is 0.1, therefore, a p-value of 0.08 would be considered statistically significant.
If the significance level is set at 0.08 what p -value would not be considered statistically significant? 0.02
0.04
0.07
0.10 The answer is d. If 8% of the result occur by chance, the significance level for the study is 0.08, therefore, a p-value of 0.10 would not be considered statistically significant.
If a hypothesis test yields a result that 85% of the results did not occur by chance, what is the p -value of this study? 0.08
0.15
0.58
0.85 The answer is b. If 85% of results did not occur by chance, therefore, 15% of the results occurred by chance and the p -value for this study is 0.15.
A researcher conducts an observational study and finds a correlation between managers’ income and the number of college credits earned. The correlation coefficient was r=.85 with a regression equation of y=515x+12000. What can you say about the relationship between these variables? a There is an association between these variables b There is a causation between these variables. c There is no relationship between these variables. d There is not enough information to determine the relationship between the variables. a) There is an association between these variables
A researcher wants to know if there was a relationship between student age and desire to complete a college degree. To answer this question, the researcher used a local community college as the sampling frame and then used stratified sampling to get a sample of students from 18 to 80 years old. Based on the information given, is there any potential bias in this study? a Yes, because the sampling frame does not match the intended population of the question. b Yes, because the sampling method will not give a representative sample. c Yes, because a voluntary sample should have been used. d No, there will likely be no bias in this study. a) Yes, because the sampling frame does not match the intended population of the question.
Using a line of best fit in slope-intercept form, y=mx+b , what must be true if there is a positive correlation? a m must be >0 . b b must be >0 . c Both m and b must be >0 . d Both m and b must have the same sign. a) m must be >0 . The answer is a. A positive correlation means the data points are following a linear pattern of going up and to the right. The line of best fit would also follow this and therefore have a positive slope
What is (are) a potential problem(s) that can occur when attempting to use regression analysis? a Extrapolation b Lurking variables c Inappropriate sampling d A, B, and C d) A, B, and C
What does it mean for a result or relationship to be statistically significant? a The relationship is not caused by mere chance. b The relationship is caused by chance. c Your hypothesis test has failed. d Your significance level is not high enough. a) The relationship is not caused by mere chance.
What technique is used to estimate the profit margin for a production level of 25 thousand units, if a line of best fit is created to estimate profit margin for production levels between 20 to 39 thousand units? a Interpolation b Linearization c Extrapolation d Internalization a) Interpolation
What must be true about the dots on a scatterplot if there is no correlation? a The dots are far away from the line of best fit. b The dots form no recognizable linear pattern. c The dots are evenly spaced around the graph. d The dots form a non-linear pattern. b) The dots form no recognizable linear pattern.
If a trend appears in a large sample of data, the trend may not be replicated if the sample is broken up into smaller subsets. What is this effect known as? a Foster’s Theorem b Bayes’ Theorem c Simpson’s Paradox d Consistency Construct c) Simpson’s Paradox
What does a strong positive correlation between two variables suggest? a The explanatory variable is increasing and the response variable is decreasing b There is an association between the variables c There is a causation between the variables d Cannot determine b) There is an association between the variables
What is the process used to create the equation for the line of best fit? a Completing the square b Least squares estimation c Fitting the line to the curve d Linear approximation b) Least squares estimation
Least squares estimation is a technique used for finding the regression line.
Consider the following equation, y=−3.2x+2.8 . What is the y -intercept for this equation? a −3.2
b 3.2
c 2.8
d −2.8 c) 2.8
A restaurant owner wants to see if she can use low temperatures to boost soup sales at her restaurant. To study a possible relationship between temperature and soup sales, she collects data throughout the year on the temperature of a given day (ranging between 20 degrees F and 90 degrees F) and the amount of soup sold that day. She performs a linear regression and comes up with a least squares regression line of y=−1.64x+176.6 with r=−0.89 where x is the temperature (in degrees F) and y is the number of daily soup sales. How much soup should she expect to sell on a day that is 50 degrees F? Round to the nearest integer. a 177 orders of soup b 95 orders of soup c 259 orders of soup d 101 orders of soup b) 95 orders of soup
What is the most appropriate definition of a scatterplot? a A graph that uses dots to demonstrate relationships between two categorical variables. b A graph where lines are shown to represent positive or negative trends. c A graph where the explanatory and response variables are plotted as ordered pairs. d A graph where a positive causation is always represented with dots forming a straight line. c) A graph where the explanatory and response variables are plotted as ordered pairs.
When linear regression is used to show there is a linear association between two variables, we know the relationship is: a A causation b A correlation c Neither A nor B d Both A and B The answer is b. A linear association between two variables is a correlation. However, we are not able to conclude that the correlation is a causation. There may be reasons why this correlation is present that do not necessarily indicate that there is a causation. For example, a lurking variable may be causing the correlation, even without a cause-and-effect relationship between the two variables being studied.
Which of the following correlation coefficients represents the weakest correlation? a −0.2
b 0.22
c 0.1
d −0.8 The answer is c. A weak correlation is represented by a correlation coefficient that is closer to 0.
A relationship between two or more variables is known as a(n) __. a) Causation b) Association c) Cause and effect d) Correlation b) Association
A researcher conducts an experimental study and finds a correlation between salary and levels of experience. The correlation coefficient was r=.75 with a regression equation of y=515x+17500 . What can you say about the relationship between these variables? a There is an association between these variables b There is a causation between these variables. c There is no relationship between these variables d There is not enough information to determine the relationship between the variables. The correct answer is b. Because this was an experimental study, there is a causation between these variables.
A researcher wants to know if there was a relationship between executive general managers’ income and the number of college credits earned. To answer this question, the researcher used a cluster sample to randomly choose 10 states across the United States; then 10 random counties were chosen; then within those 100 total counties, 4 businesses were randomly chosen; all executive general managers working within these 400 total businesses, were then invited to participate in the study. Based on the information given, is there any potential bias in this study? a Yes, because the sampling frame does not match the intended population of the question b Yes, because the sampling method will not give a representative sample. c Yes, because a voluntary sample should have been used. d No, there will likely be no bias in this study. The correct answer is d. Based on the information given, there will likely be no bias in this study.
A greater sample size improves the reliability of the least squares regression. True or False? a True b False The answer is a. This is a true statement. The larger the sample size, the greater the reliability of the least squares regression.
We find a strong correlation between two variables. Does this mean that there is a causation? a Yes b No c Only if the correlation is positive d Only if the correlation is negative The answer is b. We are not able to conclude that the correlation is a causation. There may be reasons why this correlation is present that do not necessarily indicate that there is a causation. For example, a lurking variable may be causing the correlation, even without a cause-and-effect relationship between the two variables being studied.
Which of the following statements is not a causal relationship? a The higher the temperature in the oven, the faster the food will cook. b The more miles a car is driven, the more fuel is consumed. c The time of day determines when the sun will rise. d The faster a runner goes, the shorter time it will take to complete the race. The answer is c. The time of day determining when the sun will rise is not considered a causal relationship.
What does a weak, negative correlation look like on a scatterplot? a The points follow closely along a line that moves down and to the right. b The points loosely follow a line that moves down and to the right. c The points follow closely along a line that moves up and to the right. d None of the above. The answer is b. In a weak, negative correlation, the points follow along a line that moves down and to the right, with the points being loosely dispersed along the line.
Which of the following correlation coefficients describes a strong, positive correlation? a −0.99
b 0.69
c 0.95
d 0.21 The answer is c. A strong, positive correlation is represented by a correlation coefficient that is close to 1 , such as 0.95 .
Using a line of best fit in slope-intercept form, y=mx+b , what must be true if there is a negative correlation? a m must be >0 . b m must be <0 . c Both m and b must be <0 . d Both m and b must have the opposite signs. The answer is b. While x increases, y decreases, yielding a negative slope.
Consider the following equation, y+8x=−2 . What is the y -intercept of a line with this equation? a −2
b 2
c 8
d −8 The answer is a. The slope intercept equation in simple linear regression is y=mx+b . The equation y+8x=−2 can be rewritten as y=−8x−2 . In this equation, b represents the y -intercept of the line. Therefore, the y -intercept of the line with equation y=−8x−2 is −2 .
Which correlation coefficient suggests the strongest correlation? a −0.9
b −0.3
c 0.1
d 0.8 The answer is a. The one closest to −1 or 1 is the strongest.
What should be true about the dots on a scatterplot once a line of best fit is drawn on the graph? a The y should form a perfect line. b The distance each dot is from the line is equal. c The dot furthest from the line is always an outlier. d There should be approximately the same number of dots above and below the line. The answer is d. Once the line of best fit is drawn, there should be approximately the same number of dots above and below the line.
A study is done to determine whether or not age determines salary level. The subject also records their years of experience and level of education. What is the response variable in this study? a Age b Education level c Years of experience d Salary The answer is d. The response variable in this study is the salary. The amount of salary depends on the other variables in the equation.
A restaurant owner wants to see if she can use low temperatures to boost soup sales at her restaurant. To study a possible relationship between temperature and soup sales, she collects data throughout the year on the temperature of a given day (ranging between 20 degrees F and 90 degrees F) and the amount of soup sold that day. She performs a linear regression and comes up with a least squares regression line of =−1.64x+176.6 with r=−0.89 where x is the temperature (in degrees F) and y is the number of daily soup sales. What is the correct interpretation of the slope of the regression line? a For every increase in one degree Fahrenheit, there is a corresponding increase of 1.64 sales of soup. b For every increase of one degree Fahrenheit, there is a corresponding increase of 176.6 sales of soup. c For every increase in one degree Fahrenheit, there is a corresponding decrease of 1.64 sales of soup. d For every increase of one degree Fahrenheit, there is a corresponding decrease of 176.6 sales of soup. The answer is c. Use the regression equation, which has slope −1.64. Plugging in x=0 gives y=176.6, and plugging in x=1 gives 174.96, so increasing x by 1 (1 degree Fahrenheit) decreases y by 1.64.
Inappropriate sampling can occur during regression analysis. What is (are) an example(s) of inappropriate sampling? a Non-proportional sampling b Small sample sizes c Non-random exclusion of a population subset in the sample d A, B, and C The answer is d. All of the above are examples of inappropriate sampling.
When constructing a line of best fit, what must be minimized? a The vertical distances between that line and the data points. b The length of the line. c The correlation coefficient. d The p -value. The answer is a. The line of best fit minimizes the vertical distances between that line and the data points in the scatterplot.
An experiment is the procedure to test the occurrence of an event. True or False? This is a false statement. An experiment is the procedure for which the probability of an event is calculated.
The possible results of an experiment are outcomes. True or False? Choose only one answer below. a. True b. False True Correct. This is a true statement. Each of the possible results from an experiment is known as an outcome.
The probability of an event occurring can be greater than 100%100%. True or False? Choose only one answer below. a. True b. False False Correct. This is a false statement. The probability of an event is always between 0% and 100% .
How can probability be expressed in numeric terms? Choose only one answer below. a. Fraction b. Decimal c. Percent d. All of the above d. All of the above Correct. The answer is d. Probability can be expressed as a fraction, decimal, or percent to represent the chance of an event happening.
What is an example of a fair experiment? Choose only one answer below. a. The chance of rain for the day b. The flipping of a coin c. Choosing a certain colored marble from a bag while looking into the bag d. A coin that is weighted to show “heads” more often than “tails.” b. The flipping of a coin Correct. The answer is b. This experiment has an equal probability for each possible outcome.
A union of two sets is a collection of only the elements that are listed in both of the sets. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. A union of two sets is a collection of all of the elements listed in the sets.
Consider the following two sets: A={14,15,16,17} B={11,12,13,14,16,17,18,19,20} A is a subset of B. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. By definition, to be a subset of a set, every element of the subset must be contained in the set. In this case, Set A contains 15 , which Set B does not contain. Therefore A is not a subset of set B .
In mathematics, a set is always a collection of numbers. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. In mathematics, a set is often, but not always, a collection of numbers.
Which of the following is a subset of the following set? {22,23,31,45,53,67,72,76,81,85,88,91,95,100}
Choose only one answer below. a. {31,45,53,76,81,85,88,91} Click here to select this answer b. {22,23,45,67,72,92,95,100} Click here to select this answer c. {23,31,45,53,76,81,91,95,100} Click here to select this answer d. Both A and C e. Both B and C d. Both A and C Correct. The answer is d. Both of these sets are subsets.
Consider the following sets: A={42,23,11,35,73,97,32,26,41,85,48,61,15} B={12,23,95,73,27,9,26,43,82,18,63,15,99} The intersection of A and B is: Choose only one answer below. a. {23,26,27,73} Click here to select this answer b. {15,23,61,73} Click here to select this answer c. {15,23,26,73} Click here to select this answer d. {15,26,48,73} c. {15,23,26,73} Click here to select this answer Correct. The answer is c. An intersection of two sets is a collection of the elements listed in both of the sets.
Joannie chooses a dessert recipe to bake for her book club meeting from the 25 dessert recipes she has in her recipe box. To predict the likelihood of her making a chocolate chip cookie recipe next book club meeting, would the theoretical probability 125 be most accurate? Choose only one answer below. a. Yes b. No b. No Correct. The answer is b. She likely prefers some recipes over others or more often has the ingredients at hand. To help predict the future, an empirical probability will work best.
A die is rolled 10,000 times. We would most likely expect the relative frequency of rolling a ” 1 ” to converge* on the value 16 . True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. 10,000 tosses is a large number. By the law of large numbers we would expect the relative frequency to be close to 16 , the theoretical probability.
After a certain number of trials the empirical probability of an outcome will equal the theoretical probability. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The empirical probability will always be an estimate
A researcher is testing the hypothesis that more screen time decreases a person’s ability to read social clues. The researcher is using surveys to gather information both about a person’s screen time and about his or her ability to read social clues in order to be able to predict how well a person with a certain amount of screen time will be able to read social clues. How many surveys should the researcher collect? Choose only one answer below. a. Only a few. Since the relative frequency can be used to substitute for the theoretical probability, a few surveys should give the researcher enough information to be able to make an accurate prediction. b. Some. Although relative frequency can be used to substitute for theoretical probability, the researcher will need the full range of information about screen time and ability to read social clues in order to get the full range of probabilities. c. Many. The researcher will need 100 surveys for the empirical probability estimated by relative frequency to equal the theoretical probability. Click here to select this answer d. As many as possible. The law of large numbers holds that the more trials, the closer the empirical data comes to estima d. As many as possible. The law of large numbers holds that the more trials, the closer the empirical data comes to estimating the true probability. Correct. The answer is d. There is no way to calculate the theoretical probability in a case like this. The more data the researcher gathers the clearer an idea he or she will have about the extent of its influence (if any.)
Kiki the dog has a yellow, blue, green, and orange shirt. If her owner reaches into the drawer and picks one out at random, what is the probability the shirt is NOT orange? Choose only one answer below. a. 1/4 Click here to select this answer b. 1/2 Click here to select this answer c. 3/4 c. 3/4 Click here to select this answer Correct. The answer is c. Only 1 shirt is orange and three are not orange. So the probability is 3/4 , the number of desirable outcomes (not orange) divided by the total number of possibilities.
When rolling a fair, six-sided die, what is the probability of rolling a 2 ? a) 1/6 b) 1/3 c) 2 d) 6 1/6
If you have a full, standard deck of cards, what is the probability of selecting a queen of hearts? a) 1/52 b) 1/26 c) 1/13 d) 1/4 1/52
You have a jar of 7 marbles: 1 red marble, 2 green marbles, and 4 blue marbles. Selecting a marble at random, what is the probability that you select a green marble? a) 1/7 b) 2/7 c) 3/7 d) 4/7 2/7
You examine the number of times a player hit a home run this season, divided by the number of at-bats the player had. What is this an example of? a) Theoretical Probability b) Empirical Probability c) The Law of Large Numbers d) All of the above b) Empirical Probability Correct. The answer is b. We are using the number of times an event occurred to estimate the probability, therefore this is an example of empirical probability.
The Cardinals have won 100 of their 162 games. Using only this data, what is the probability that the Cardinals win a game? a) 100/162 b) 50/81 c) 62% d) All of the above. d) All of the above.
When rolling a fair, six-sided die, what is the probability of rolling a 2 or a 3? a) 1/6 b) 1/3 c) 1/2 d) 2/3 1/3
Any experiment or trial will have only one sample space. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. A sample space is the set of outcomes for one particular experiment, so any experiment has one unique sample space.
All events in the sample space have the same relative frequency. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The relative frequency of an event is how often it happens in practice. For example, we do not know if TechTown’s customers that purchased desktops selected models with 1920×1080 p displays more often than models with 1366×768 p displays until we gather data. It is reasonable to assume, however, that the relative frequency of customer purchases (desktops with 1920×1080 p displays versus desktops with 1366×768 p displays) might not be equal.
In a tree diagram showing the sample space of an experiment, each new option increases the sample size. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. Each new option will be added to each of the previous options, increasing the size of the sample space dramatically.
A list, table, or tree diagram will show the exact same sample space. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. No matter the method used, each technique will result in the same sample space.
The sample space and sample size represent the same thing. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The sample space is a set of outcomes while the sample size is the number of different outcomes.
The sample space can have equally likely outcomes. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. Each outcome in a sample space can have the same chance of occurring.
The probability using sample spaces with equally likely outcomes is the number of outcomes in the event divided by the sample size. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The probability is the number of outcomes in the event divided by the sample size.
Using a tree diagram can result in probability greater than 1 . True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The probability of an event can never be greater than 1 .
A tree diagram is the only method to determine the probability of an event. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. A list, table, tree diagram, and other methods can help determine the probability of an event.
Finding the probability of events, given all outcomes are equally likely, has limited applications. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. Most probabilities are calculated when there are not equally likely outcomes.
The complement of an event occurring is the event not occurring. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The opposite of an event happening is the event not occuring.
If two events have no common outcomes, they are complementary. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. Two events with no common outcomes are complementary only if their union is the whole universe.
If the probability of the event given is 0 , then the complementary event will have probability equal to 1 . True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The sum of the probabilities of the event and its complement is 1, so if the probability of the given event is zero, its complement has probability equal to 1.
Complementary events occur whenever there are two events. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The two events must be defined events.
The sum of all probabilities of individual outcomes in the sample space must equal 1 . True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The sum of all probabilities of individual outcomes equals 1 .
When researching or trying to learn something about a given population, the population and the sample should always be disjoint. True or False? Choose only one answer below. a. True b. False b. False
Correct. This is a false statement. While a population and a sample can be disjoint, they shouldn’t be if you’re trying to use your sample to learn something about your population!
A sample space S is comprised of 13 equally likely outcomes. Suppose event E contains 5 of those outcomes.The probability of E is 5/13 . True or False? Choose only one answer below. a. True b. False true
The addition rule for disjoint events would yield the same result as the general formula for theoretical probability, counting the ways of getting a certain result. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. We have done problems both ways in this module. We add the individual probabilities for the disjoint events of, say, being born in February OR being born in April. Or we count up all the “ways” of being born in either February or April and put that number over the total size of the sample space. Either method for this problem would yield 2/12=1/6 .
If 2 events can occur at the same time, they are called disjoint. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. Disjoint events are 2 events that cannot occur at the same time.
If two events are disjoint there is no intersection between the events. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. There are no common elements between 2 disjoint events.
A frequency table consists of two categorical variables. True or False? Choose only one answer below. a. True b. False true
A frequency table is read by the row and column entries. True or False? Choose only one answer below. a. True b. False true
The only information you need to perform analysis in a two-way table can be provided by row entries. True or False? Choose only one answer below. a. True b. False false
Relative frequency helps determine if an event is independent. True or False? Choose only one answer below. a. True b. False True Correct. This is a true statement. The relative frequency is related to the independence of events.
The frequency table does not need labels for rows or columns. True or False? Choose only one answer below. a. True b. False false
The probability of going fishing on a Saturday is represented as P(F) . The probability of catching a fish on a Saturday is P(C) . How would we write the probability of catching a fish on a Saturday, given that you have gone fishing? Choose only one answer below. a. P(C&F) Click here to select this answer b. P(F|C) Click here to select this answer c. P(C|F) c. P(C|F) Click here to select this answer Correct. The answer is c. This is read as “the probability of catching a fish, given that you have gone fishing.”
There is a jar with 11 marbles: seven red marbles and four green ones. Your sister then takes a red marble and still has it. What is now the probability of choosing a green marble, if you select a marble at random? Choose only one answer below. a. 4/10 Click here to select this answer b. 4/11 Click here to select this answer c. 3/11 Click here to select this answer d. 3/10 4/10
If the probability of having blond hair is 5% , then the probability of having blond hair, given that you are Swedish, is 5% . True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. Being Swedish and having blond hair are dependent events, as Swedes are more likely to have blond hair.
What are dependent events? Choose only one answer below. a. Not independent b. The occurrence of one affects the probability of the other c. All of the above c. All of the above
Correct. The answer is c. Dependent events are not independent by definition. The probability of a dependent event is also dependent on another event. Therefore, all of the above is correct.
Conditional probability does not rely on another event happening. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. Conditional probability is the probability of an event occurring after one event has happened.
What is conditional probability? Choose only one answer below. a. Probability of one event b. Probability of two events occurring, individually. c. Probability of an event occurring given that another event has already occurred. d. All of the above c. Probability of an event occurring given that another event has already occurred. Correct. The answer is c. Conditional probability is the probability of an event occurring given that another event has already occurred.
For dependent events, the probability of B is always equal to the probability of B , given A . True or False? Choose only one answer below. a. True b. False b. False Correct. For dependent events, the probability of B is not equal to the probability of B , given A .
The intersection is always used for conditional probability. True or False? Choose only one answer below. a. True b. False a. True Correct. This statement is true. Conditional probability does use the intersection.
P(B|A)=P(A and B) . True or False? Choose only one answer below. a. True b. False false
The probability of two independent events both occurring is P(A)+P(B) . True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The probability of 2 independent events both occurring is P(A)×P(B) .
Which statement does not belong for two independent events? Choose only one answer below. a. P(A and B)=P(A)⋅P(B) Click here to select this answer b. P(A|B)=P(B) Click here to select this answer c. P(B|A)=P(B) Click here to select this answer d. P(B|A)=P(B|not A) b. P(A|B)=P(B) Click here to select this answer Correct. The answer is b. The correct statement is P(A|B)=P(A) .
The probability of the union of two dependent events is P(A)+P(B|A) . True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The probability is P(A)+P(B)−P(A and B) .
Two events can be independent and dependent. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. Two events can be either independent or dependent.
Independence can be determined from any of the four given statements below: P(A and B)=P(A)⋅P(B) P(A|B)=P(A) P(B|A)=P(B) P(B|A)=P(B|not A) True or False? Choose only one answer below. a. True b. False true
What do we call events where the occurrence of one event does not affect the probability that the other event will occur? a) Independent events b) Dependent events c) Mutually exclusive events d) All of the above a) Independent events Correct. The correct answer is a. If the occurrence of one event does not affect the probability that the other event will occur, they are known as independent events.
You select one card from a deck of cards, and do NOT place that card back in the deck. Then, you select a second card from the deck of cards. Determine if the following two events are independent or dependent: Selecting a queen and then selecting a king. a) Independent b) Dependent dependent
For independent events, what does P(A and B) equal? a) P(A)⋅P(B) b) P(A) c) P(B) d) P(B|not A) a) P(A)⋅P(B)
A and B are independent events. P(A)=1 and P(B)=0.1 . Calculate P(A and B) . a) 0.01 b) 0.1 c) 1 d) 1.1 b) 0.1
Correct. The correct answer is b. P(A and B)=P(A)⋅P(B)=1⋅0.1=0.1
A and B are independent events. P(A)=0.3 and P(B)=0.8 . Calculate P(A|B) . a) 0.24 b) 0.3 c) 0.8 d) 1.1 b) 0.3
A and B are independent events. P(A)=0.5 and P(B)=1 . Calculate P(B|A) . a) 0.5 b) 1 c) 1.5 d) 1/5 b) 1 Correct. The correct answer is b. P(B|A)=P(B)=1 .
Frequency tables can estimate the probability of an event. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The table can be used to estimate the probability of an event.
The totals in a row or column can be used to find the probability of an event in a frequency table. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The probability of an event can be determined by using the totals of a row or column.
The probability of only one event can be determined from a frequency table. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The probabilities of many events can be determined from a frequency table.
A frequency table has only 2 rows and 2 columns. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. A frequency table can have more than 2 rows and 2 columns.
A frequency table can have a different number of rows and columns. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The frequency table can have an unequal number of rows and columns.
A probability tree has the same information as a tree diagram. True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. A probability tree contains the probability of an event, not just which events occur.
A probability tree can be used to compare the probabilities of different events. True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. The probability tree can compare different probabilities.
The sum of the probabilities on a probability tree do not equal 1 . True or False? Choose only one answer below. a. True b. False b. False Correct. This is a false statement. The sum of probabilities on all levels is 1 .
The law of total probability is the sum of the product of all sequences of possible outcomes in a sample space is 1 . True or False? Choose only one answer below. a. True b. False a. True Correct. This is a true statement. In a probability tree, multiply each branch of the tree and the sum of the products is 1 .
