YESHIVA UNIVERSITY ISDS 361A FINAL EXAM 2024
The collection of all units of interest in a particular study is called
a. Sample
b. Parameter
c. Population
d. Statistic – correct answer✔✔ Population
Suppose there is a dataset of baseball scores from several matches between the Seattle Mariners and
Anaheim Angels. A statistician wants to summarize the data using graphical and numerical measures.
What branch of Statistics will she need to use?
a. Descriptive Statistics
b. Inferential Statistics – correct answer✔✔ Descriptive Statistics
Which of these is not a measure of variability?
a. Mean
b. Standard deviation
c. IQR
d. Range – correct answer✔✔ Mean
A histogram with a long left tail is said to be
a. Symmetric
b. Bell-shaped
c. Positively skewed
d. Negatively skewed – correct answer✔✔ Negatively skewed
For a positively skewed distribution
a. Mean is smaller than median
b. Mean is equal to the median
c. Mean is greater than the median
d. None of the above – correct answer✔✔ Mean is greater than the median
A standard normal distribution is one that has
a. Zero mean and zero variance
b. Zero mean and constant variance
c. Constant mean and variance = 1
d. Zero mean and variance = 1 – correct answer✔✔ Zero mean and variance = 1
For a random variable X with mean = 10 and variance = 25, what is P(X > 20)?
a. P(Z > 2)
b. P(Z < 2) c. P(Z > 0.4)
d. P(Z > -0.4) – correct answer✔✔ P(Z > 2)
Which theorem or rule helps determine the sampling distribution of the sample mean?
a. Chebyshev’s Theorem
b. Central Limit Theorem
c. Empirical Rule
d. None of the above – correct answer✔✔ Central Limit Theorem
How does the standard error of the sampling distribution behave as the sample size (n) increases?
a. Decreases
b. Increases
c. Stays unchanged
A histogram is bi-modal. Then,
a. It has one mode
b. It has two modes
c. It has three modes
b. It has two modes
A histogram is symmetric. Then,
a. It has no skewness
b. It has only one mode
c. It is mean is greater than median
a. It has no skewness
A histogram of a given data shows three clear peaks. This may mean that
a. There are three distinct groups in the data
b. There are three modes in the data
c. Both a and b are correct
c. Both a and b are correct
A value has z-score of 3. This means that
a. That value if 3 standard deviation below the mean
b. That value if 3 standard deviation above the mean
c. That value is 3 standard deviation to the right of the median
b. That value if 3 standard deviation above the mean
A variable has Q1 of 25 and Q3 of 75. It has also a Q2 of 50. The IQR is
a. 25
b. 50
c. -50
b. 50
From a random sample of 500 students, students study for an average of 10 hours per week with a standard deviation of 4 hours per week. Say, a student in this sample studies for 12 hours per week. What is the z-score of this student?
a. 2
b. 0.5
c. 8
b. 0.5
In a statistics mid-term exam graded out of 100 points, the distribution of the exam scores was bi-modal with a mean of 70 points with a standard deviation of 10 points. What percentage of students scored between 40 points and 100 points?
a. At least 70%
b. at least 89%
c. approximately 100%
b. at least 89%
Q2 is also known as
a. Mean
b. Median
c. Mode
b. Median
Students at a liberal arts college study for an average of 10 hours per week with a standard deviation of 4 hours per week. The distribution of their study time happens to be skewed to left. At least 75% of students study between 2 and B hours a week. What is the value of B?
a. 18 hours
b. 2 hours
c. 4 hours
d. None of the above
a. 18 hours
Students at a liberal arts college study for an average of 10 hours per week with a standard deviation of 2 hours per week. The distribution of their study time happens to be uni-modal, symmetric and bell shaped. Approximately 68% of students study between 8 and B hours a week. What is the value of B?
a. 12 hours
b. 16 hours
c. 14 hours
d. None of the above
a. 12 hours
The histogram of a quantitative variable is positively skewed. The mean of the variable is 35. Which one of the following is a more likely value of the median?
a. 55
b. 30
c. 35
b. 30
The histogram of a variable is symmetric, uni-modal and mound shaped. Then,
a. Mean > median
b. Mean < Median
C.Mean = Median
C.Mean = Median
When using a box-plot, a value outside of the whisker is considered
a. Median
b. Outlier
c. Standard Deviation
b. Outlier
X has a normal distribution with mean µ = 20 and standard deviation σ = 5. Match the following probability statement with the corresponding statement regarding Z: P(X > 25).
a. P(Z = 1)
b. P(Z > 1)
c. P(Z < 1) d. P(Z > 2)
b. P(Z > 1)
For a standard normal variable Z, compute P(Z < 1.5). Round your answer to two decimal places.
a. 0.09
b. 0.07
c. 0.92
d. 0.93
d. 0.93
Let X have a normal distribution with mean µ = 30 and standard deviation σ = 10. Calculate P(X > 40), and round your answer to two decimal places.
a. 0.65
b. 0.84
c. 0.16
d. 0.11
c. 0.16
Let X have a normal distribution with mean µ = 30 and standard deviation σ = 10. Calculate P(30 < X < 40), rounding your answer to two decimal places.
a. 0.34
b. 0.46
c. 0.30
d. 0.43
a. 0.34
Given that Z is a standard normal variable, P(Z > 1.61) is (rounding to two decimal places):
a. 0.77
b. None of the above choices
c. 0.05
d. 0.95
c. 0.05
What is the shape of a normal curve?
a. Symmetric
b. Positively skewed
c. None of the above
d. Negatively skewed
a. Symmetric
Most values of a standard normal distribution lie between:
a. 1 and 3
b. -3 and +3
c. 0 and 3
d. 0 and 1
b. -3 and +3
Which of the following is not a characteristic of a normal distribution?
a. It is symmetrical
b. It is a bell-shaped distribution
c. The mean is always zero
d. The mean, median and mode are all equal
c. The mean is always zero
A larger standard deviation of a normal distribution indicates that the distribution becomes
a. more skewed to the right
b. flatter and wider
c. more skewed to the left
d. narrower and more peaked
b. flatter and wider
The Excel function that is used to calculate normal probabilities for Z is
a. norm.s.dist
b. normal
c. norm.inv
d. norm.dist
a. norm.s.dist
The standard deviation of the sampling distribution of the sample mean is also called
a. central limit theorem
b. population standard deviation
c. standard error
d. None of the above
c. standard error
The mean of the sampling distribution of the sample mean is:
a. equal to the population mean
b. greater than the population mean
c. less than the population mean
d. not equal to the population mean but the direction cannot be determined
a. equal to the population mean
A random sample of size 49 is taken from a population whose mean is 300 and standard deviation is 21. The mean and the standard error of the sampling distribution of the sample mean, respectively are:
a. 300 and 21
b. 300 and 3
c. 300 and 0.43
d. None of the above
b. 300 and 3
Given an infinite population with a mean of 40 and a standard deviation of 15, a sample of size 100 is taken from it. The standard error of the sampling distribution of the sample mean is:
a. 15
b. 0.15
c. 1.5
d. None of these choices
c. 1.5
If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean will be:
a. Normal for all values of n
b. Normal only for n > 30
c. Approximately normal for all values of n
d. Approximately normal for all values of n > 30
a. Normal for all values of n
For a random sample of size 50 drawn from a population, what theorem or rule is used to determine the type of distribution for the sampling distribution of the sample mean?
a. Central Limit Theorem
b. Chebyshev’s theorem
c. Empirical Rule
d. None of the above
a. Central Limit Theorem
Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, is less than 78 is:
a. 0.9332
b. 0.5987
c. 1.5000
d. 0.0668
a. 0.9332
A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12 respectively. The probability that the sample mean is larger than 70 equals:
a. P(Z > 70)
b. P(Z > 2)
c. P(Z > 0.17)
d. P(Z > 1.05)
d. P(Z > 1.05)
A sample of 250 observations is selected at random from a n infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion will be:
a. 0.5000
b. 0.0274
c. 0.0316
d. 0.0548
b. 0.0274
A sample of size 200 is taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion is less than 0.58 is:
a. 0.719
b. 0.580
c. 0.762
d. 0.281
d. 0.281
Confidence interval is obtained as
a. point estimate ± critical value
b. point estimate ± standard error
c. point estimate ± margin of error
c. point estimate ± margin of error
Given the sample proportion (p ̅) and sample size, n, we wish to obtain the confidence interval estimate of the population proportion (p). The margin of error of the confidence interval estimate is obtained as
a. z(α/2) ×√((p(bar)(1-(p(bar))))/n)
b. z(α/2) ×√((p(1-p))/n)
a. z(α/2) ×√((p(bar)(1-(p(bar))))/n)
Margin of error is obtained as
a. point estimate ± critical value
b. critical value × standard error
c. point estimate × critical value
b. critical value × standard error
Suppose (1-α)=0.9. The critical value, zα/2 , is obtained in Excel using
a. -NORM.S.INV(0.05)
b. -NORM.S.INV(0.1)
c. -NORM.S.INV(0.2)
a. -NORM.S.INV(0.05)
Suppose (1-α)=0.95 and n = 20. The critical value tα/2, can be obtained in Excel using
a. -T.INV(0.025, 19)
b. -T.INV(0.05, 19)
c. -T.INV(0.1, 19)
a. -T.INV(0.025, 19)
Suppose σ=36 and sample size n = 81. What is the standard error (S.E) of x ̅?
a. 0.45
b. 4
c. 13.5
b. 4
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