Chapter 7, Sampling Distributions Video Solutions, Introduction to Probability and Statistics

Problem 1

A population consists of $N=500$ experimental units. Use a random number table to select a random sample of $n=20$ experimental units. (HINT: Since you need to use three-digit numbers, you can assign 2 three-digit numbers to each of the sampling units in the manner shown in the table.) What is the probability that each experimental unit is selected for inclusion in the sample?

Sheryl Ezze

Numerade Educator

02:06

Problem 2

A political analyst wishes to select a sample of $n=20$ people from a population of $2000 .$ Use the random number table to identify the people to be included in the sample.

Harsh Gadhiya

Numerade Educator

02:25

Problem 3

A population contains 50,000 voters. Use the random number table to identify the voters to be included in a random sample of $n=15$.

Raymond Matshanda

Numerade Educator

02:25

Problem 4

A small city contains 20,000 voters. Use the random number table to identify the voters to be included in a random sample of $n=15$.

Raymond Matshanda

Numerade Educator

01:35

Problem 5

Every 10th Person A random sample of public opinion in a small town was obtained by selecting every 10th person who passed by the busiest corner in the downtown area. Will this sample have the characteristics of a random sample selected from the town's citizens? Explain.

Varsha Aggarwal

Numerade Educator

01:54

Problem 6

Parks and Recreation A questionnaire was mailed to 1000 registered municipal voters selected at random. Only 500 questionnaires were returned, and of the 500 returned, 360 respondents were strongly opposed to a surcharge proposed to support the city Parks and Recreation Department. Are you willing to accept the $72 \%$ figure as a valid estimate of the percentage in the city who are opposed to the surcharge? Why or why not?

Varsha Aggarwal

Numerade Educator

02:05

Problem 7

Lists In many states, lists of possible jurors are assembled from voter registration lists and Department of Motor Vehicles records of licensed drivers and car owners. In what ways might this list not cover certain sectors of the population adequately?

Varsha Aggarwal

Numerade Educator

02:02

Problem 8

One question on a survey questionnaire is phrased as follows: "Don't you agree that there is too much sex and violence during prime TV viewing hours?" Comment on possible problems with the responses to this question. Suggest a better way to pose the question.

Varsha Aggarwal

Numerade Educator

01:06

Problem 9

Contrary to current thought about omega- 3 fatty acids, new research shows that the beneficial fats may not help reduce second heart attacks in heart attack survivors. The study included 4837 men and women being treated for heart disease. The experimental group received an additional $400 \mathrm{mg}$ of the fats daily. ${ }^{1}$ Suppose that this experiment was repeated with 50 individuals in the control group and 50 individuals in the experimental group. Determine a randomization scheme to assign the 100 individuals to the two groups.

Charles Machakwa

Numerade Educator

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Problem 10

Does the race of an interviewer matter? This question was investigated by Chris Gilberg and colleagues and reported in an issue of Chance magazine. $^{2}$ The interviewer asked, "Do you feel that affirmative action should be used as an occupation selection criteria?' with possible answers of yes or no.
a. What problems might you expect with responses to this question when asked by interviewers of different ethnic origins?
b. When people were interviewed by an AfricanAmerican, the response was about $70 \%$ in favor of affirmative action, approximately $35 \%$ when interviewed by an Asian, and approximately $25 \%$ when interviewed by a Caucasian. Do these results support your answer in part a?

Victor Salazar

Numerade Educator

01:58

Problem 11

The American Journal of Human Biology reported on a study of a dietary assessment tool for use in the population of urban Native American youth. ${ }^{3}$ The subjects were Native American youth attending an after-school program in Minneapolis, MN. All 61 children between the ages of 9 and 13 who satisfied the requirements of the study objectives were included in the experiment.
a. Describe the sampling plan used to select study participants.
b. What chance mechanism was used to select this sample of 61 Native American 9 - to 13 -year-old individuals?
c. Can valid inferences be made using the results of this study? Why or why not?
d. If you had to devise an alternative sampling plan, what would you change?

James Kiss

Numerade Educator

03:10

Problem 12

A small new study shows that tai chi, an ancient Chinese practice of exercise and meditation, may relieve symptoms of chronic painful fibromyalgia. The study assigned 66 fibromyalgia patients to take either a 12 -week tai chi class, or attend a wellness education class.
a. Provide a randomization scheme to assign $66 \mathrm{sub}$ jects to the two groups.
b. Will your randomization scheme result in equal sized groups? Explain.

Varsha Aggarwal

Numerade Educator

01:34

Problem 13

Going to the Moon Two different Gallup Polls were conducted for CNN/USA Today, both of which involved people's feelings about the U.S. space program. ${ }^{5}$ Here is a question from each poll, along with the responses of the sampled Americans:
a. Read the two poll questions. Which of the two wordings is more unbiased? Explain.
b. Look at the responses for the two different polls. How would you explain the large differences in the percentages either favoring or opposing the new program?

Varsha Aggarwal

Numerade Educator

05:54

Problem 14

A 2003 nationwide policy survey titled "Ask America" was sent by the National Republican Congressional Committee to voters in the Forty-fourth Congressional District, asking for opinions on a variety of political issues. ${ }^{6}$ Here are some questions from the survey:
- In recent years has the federal government grown more or less intrusive in your personal and business affairs?
- Is President Bush right in trying to rein in the size and scope of the federal government against the wishes of the big government Democrats?
- Do you believe the death penalty is a deterrrent to crime?
- Do you agree that the obstructionist Democrats should not be allowed to gain control of the U.S. Congress in the upcoming elections?
Comment on the effect of wording bias on the responses gathered using this survey.

Robin Corrigan

Numerade Educator