CHAPTER 9 EXERCISES
There are four sets of exercises for Chapter 9.
Exercise 9.1 Reviewing Polling Data reports a poll on racial discrimination. This exercise is designed to give you practice in computing and interpreting sampling statistics.
Exercise 9.2 Attitudes toward Corporal Punishment: Are Men and Women Different? examines data to compare men’s and women’s attitudes about spanking. This exercise is designed to give you practice in interpreting a contingency table and a test of statistical significance.
Exercise 9.3 What Is Going On in the Schools? considers a study to see if African American and Hispanic students are more likely to be suspended than other students. This exercise is designed to give you practice in interpreting tests of statistical significance.
Exercise 9.4 How Groups Work Together presents data comparing perceived characteristics of collaborations formed around women’s issues and environmental issues. This exercise is designed to give you practice in interpreting tables that report the results of t-tests.
EXERCISE 9.1 Reviewing Polling Data
Scenario
You are a member of a community action group that focuses on various issues that affect community life. As you are perusing the Web for data on incidents of racial discrimination, you find a Washington Post–ABC poll of 1,079 randomly selected Americans. Two hundred and four of the poll respondents were African Americans.
Section A: Getting Started
1. The following data were reported in answer to the question “How big a problem is racism in our society today?”
Of all respondents: 26% a “big problem,” 22% a “small problem”
Of African American respondents: 44% a “big problem,” 11% a “small problem”
Of White respondents: 22% a “big problem,” 23% a “small problem”
a. Use the reported statistics, for example, 26%, to estimate p and 1 – p. Compute the sampling error for the entire sample, the African American sample, and the White sample. (Assume that the number of Whites is the same as the number of non–African Americans.)
b. Use the sampling error and report the confidence interval for the percentage of African Americans and Whites who believed that racism was a big problem.
c. What is the probability that your estimates in 1b are wrong? How did you arrive at this estimate?
2. Assume maximum variability (50-50 split)
a. Compute the sampling errors for the entire sample and for the 204-member African American sample.
b. As a general practice, would you analyze survey data using a 50-50 split or would you use the statistical analysis (question 1) to come up with more precise estimates? Justify your answer.
3. The survey also reported that among African American respondents 60 percent had personally felt that “a shopkeeper or sales clerk was trying to make” them feel unwelcome. You are curious if the same thing is true in your community. In trying to decide a value of p would you use 0.60, 0.50, or something else? Justify your answer.
4. The community action group considers replicating parts of a survey. What size sample is needed to have 2 percent, 5 percent, or 10 percent accuracy? (Note that accuracy is the same as sampling error.)
EXERCISE 9.2 Attitudes toward Corporal Punishment: Are Men and Women Different?
Scenario
A child care organization commissioned a random survey to identify attitudes toward child-raising. A topic of interest was the difference between the beliefs of men and women regarding discipline. The follow table reports data on men’s and women’s attitudes toward spanking.
Attitudes toward Spanking by Respondent Gender
Favor Spanking Male Female
Strongly 115 107
Somewhat 212 221
Oppose 73 109
Strongly oppose 18 42
Chi-square = 13.1, degrees of freedom = 3, significance = 0.004.
Section A: Getting Started
1. State the alternative hypothesis and the null hypothesis that could be tested with the data in this table.
2. Identify the independent and the dependent variables.
3. Calculate percentages and include in them in a table. Write a sentence to describe the relationship shown in the table. Do the data in the table support or contradict your hypothesis? Explain.
4. Based on the chi-square evidence what would you do, that is, would you reject the null hypothesis?
Section B: Small Group Exercise
1. What are the implications of the findings presented in exercise 9.2? Do you consider the table an interesting observation, a question for further study, or something else?
2. A finding of statistical significance can be persuasive. What other evidence should the child care organization present so that parents and other stakeholders are able to evaluate the findings?
EXERCISE 9.3 What Is Going On in the Schools?
Scenario
A community action group has heard complaints that African American and Hispanic students are more likely to be suspended (either in-school or out-of-school) than other students. The superintendent of schools offers to review the files of students in grades 9–12. The school system has 39,000 students in grades 9–12: 58 percent African American, 12 percent Hispanic, and 25 percent White.
Section A: Getting Started
1. What target population would you recommend the superintendent use? Why did you recommend this population? (Note that target population refers to the specific population that the data will represent.)
2. State the alternative hypothesis and the null hypothesis the superintendent should test.
3. If the superintendent tests the hypothesis and makes a Type I error, explain what has happened.
4. If the superintendent tests the hypothesis and makes a Type II error, explain what has happened.
5. Should the superintendent be more concerned about a Type I error or a Type II error? Justify your answer.
6. The superintendent originally set α = 0.05. How can she further decrease the probability of a Type I error? How can she further decrease the probability of a Type II error?
Section B: Small Group Exercise
1. Decide on a target population and suggest a sample size for the superintendent’s study. Justify your recommendation.
2. Discuss what actions the superintendent might take if the null hypothesis is rejected.
3. List arguments for the position
a. Committing a Type I error is the more serious concern.
b. Committing a Type II error is the more serious concern.
4. Based on what you have observed in Exercises 9.2 and 9.3 draft a memo “What you want to know about statistical significance: A guide for citizens.”
EXERCISE 9.4 How Groups Work Together
The following table was created as part of a study of collaborations formed around women’s issues and environmental issues. Members answered a series of questions to see if the coalitions were different. Each question was answered along a scale ranging from 1 = Not at all true to 7 = To a great extent true.
Two-tailed t-test: * p < 0.05, ** p < 0.05, *** p < 0.001.
Section A: Getting Started
1. In plain English explain what information the table contains.
2. In plain English interpret the statistical information for the last line .
3. How do collaborations focused on women’s issues differ from collaborations focused on environmental issues? What criteria did you use to make your choices?
