CHAPTER 1 STATISTICS

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CHAPTER 1 ∇ STATISTICS

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The purpose of Chapter 1 is to present:

• an initial image of statistics that includes both the key role statistics has in the technical aspects of

life as well as its everyday applicability,

• its basic vocabulary and definitions,
• basic ideas and concerns about the processes used to obtain sample data.

Section 1, at the beginning of each chapter, primes the student for the concepts that will be presented in the chapter. It is our hope that the students, after completing study of the chapter, will see more clearly the meaning of the statistics reported and will recognize this change in the clarity of their interpretation.The exercises in this first section are also excellent introductions to statistics and how they can be presented. The differences, similarities, sources of information, sample sizes (if given), and so on should be pointed out to the students.This discussion, in addition to the learning of basic statistical terminology (as presented in Chapter 1), prepares the student to find and question everyday statistical presentations. Bring in newspapers and/or magazines and have groups of students find a form of statistics whether it be a graph, percentage, average, and so on. This raises their awareness and reinforces the concepts.Encourage students to bring in their own examples for possible extra credit projects.

(Elementary Statistics 11e Robert Johnson Patricia Kuby) (Solution Manual, For Complete File, Download link at the end of this File) 1 / 4

Chapter 1: Statistics 2

SECTION 1.1 EXERCISES

1.1 a. How often do you eat fruit?

• Internet visitors at the Postyour.info website.
• 63
• 1/63 = 0.01587, 11/63 = 0.1746, 16/63 = 0.25397
• No. Only people who visited the site and wanted to answer the question did so.

1.2 a. Answers will vary.

• It does not appear, based on the list of averages given, that Java professionals work a 40-hour week.
• Only if long work hours are desirable.

1.3 a. Americans

• length of time before a Wifi user gets antsy and needs to check their messages
• 47% of those people surveyed say they get antsy within one hour about checking their email, etc.

1.4 a. Answers will vary

• 5% of those asked replied that they made their bed weekly.

1.5 Answers will vary

There are many new definitions introduced in this section. Include examples that the students can relate to, such as, 'average age of a student at our college.' Carry this through each of the definitions. Skillbuilder Applet Exercises 1.21 and 1.32 demonstrate the concepts visually.Students also have difficulty with the difference between variable and data.Exercises 1.35 and 1.36 are good for classroom discussion. The instructor will need to determine whether or not the students understand the basic concepts.

SECTION 1.2 EXERCISES

The articles in Applied Example 1.2 gives information about the sample (the number of people surveyed).Be watchful of articles that do not give any of this information. Sometimes not knowing something about the sample or survey size causes a question of credibility.

1.6 Answers will vary. 2 / 4

3 Chapter 1: Statistics

Descriptive Statistics - refers to the techniques and methods for organizing and summarizing the information obtained from the sample.Inferential Statistics - refers to the techniques of interpreting and generalizing about the population based on the information obtained from the sample.

1.7 a. inferential b. descriptive

1.8 a. descriptive b. inferential

1.9 a. married women, ages 25-50, who have 2 or more children

• 1,170
• how often moms say they have a date night with their spouse
• 18% of those surveyed say they have a date night every 4-6 months
• (0.18)(1170) = 211

1.10 a. American adults

• 777
• spring-cleaning chore he or she would prefer to hire someone to do
• 777(0.47) = 365
• actual percentage for the whole population could be from 3.52% lower to 3.52% higher than the

percentage reported

• between 8.48% and 15.52%

1.11 a. USA teens

• 501
• what everyday invention they thought would be obsolete in 5 years
• 501(0.21) = 105
• actual percentage could be 4.3% lower or 4.3% higher than quoted
• between 16.7% and 25.3%

A variable is the characteristic of interest (ex. height), where data is a value for the variable (ex. 5'5"). A variable varies (heights vary), that is, heights can take on different values. Data (singular) such as 5'5" (one person's height) is constant; it does not change in value for a specific subject.An attribute variable can take on any qualitative or "numerical" qualitative information (ex. kinds of fruit, types of music, religious preference, model year - most answers are in words, although model year would have "numerical" answers such as "2010"). An attribute variable can be nominal (description or name) or ordinal (ordered position or rank; first, second,…).

A numerical variable can take on any quantitative information. This includes any count-type and measurable- type data (ex. number of children in a family, amount of time, age, height, area, volume, miles per gallon). A numerical variable can be discrete or continuous. The domain of a discrete variable has gaps between the possible values; there are numerical values that cannot occur. Theoretically, the domain of a continuous variable has no gaps since all numerical values are possible. Do not be confused by data that has been rounded due to scale being used or for convenience reasons. 3 / 4

Chapter 1: Statistics 4

1.12 a. all Americans consumers or all American taxpayers

• tax return consumers
• ‘action’ upon receipt of tax refund
• pay down debt, longest bar

1.13 a. 45% (100% - 55%) b. The percentages are from different groups.

1.14 a. Yes, if the rate increases from 4% to 6% that is a 50% increase in the rate: (6-4)/4 = 2/4 = 0.50 = 50%.As a percent alone; the 50% is meaningless, it does not give the actual size of the numbers involved.

• The phrase “50% jump” works much more effectively at getting people’s attention than does “2%

increase.”

Population - the collection of all individuals, objects, or scores whose properties are under consideration.Parameter - a number calculated from the population of values.Sample - that part of the population from which the data values or information is obtained.Statistic - a number calculated from the sample values.

NOTE: Parameters are calculated from populations; both begin with p.

Statistics are calculated from samples; both begin with s.

1.15 a. The population is all US adults.

• A sample is the 1200 randomly selected adults.
• The variable is “allergy status” for each adult.
• The statistic is the 33.2% based on the sampled adults.
• The parameter is the percent of all US adults who have an allergy, in this case, 36%.

1.16 Answers will vary.

1.17 Parameters give the information for the entire population and have one specific value. Statistics come from samples which can vary in size and method of data collection, therefore giving different measurements for each different sample.

1.18 A football jersey number is a categorical variable. It is attribute information that can identify something about the position played by a player [for example; 60’s & 70’s are numbers for lineman and they are not eligible to catch passes, other number groups have similar restrictions], but does not give any measurable information about that player.

1.19 a. Attribute possibilities: marital status, ZIP code, gender, highest level of education

• Numerical possibilities: annual income, age, distance to store, amount spent
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