Exam 15: More About Inference for Categorical Variables

Use the following information for questions: In the 1994 General Social Survey, a nationwide survey done every other year in the United States, the 1,185 respondents who had ever been married were asked the age at which they first wed and whether they had ever been divorced. The two-way table below summarizes the observed counts for the relationship between "age first wed" (categorized into four age groups) and "ever divorce" (no or yes). A chi-square value and p-value are given below the table. -What is the expected count for the "Under 20" and "No" cell?

Use the following information for questions: In the General Social Survey, respondents were asked what they thought was most important to get ahead: hard work, lucky breaks, or both. Minitab output for 1026 respondents, by gender, is shown below: -What is the value of the test statistic?

Use the following information for questions: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. -What percentage of female respondents has a graduate degree?

A chi-square test involves a set of counts called "expected counts." What are the expected counts?

Use the following information for questions: Students in a statistics class were asked, "With whom do you find it easier to make friends: person of the same sex, person of opposite sex, or no preference?" A table summarizing the responses by gender is given below. Minitab results for a chi-square test for these data were "Chi-Sq = 7.15 p-value = 0.028. -What are the degrees of freedom for this situation?

Use the following information for questions: In the General Social Survey, respondents were asked "If your party nominated a woman for President, would you vote for her if she were qualified for the job?" A two-way table summarizing the results for 953 respondents, by gender, is shown below: -The chi-square test statistic = 3.35. What is the p-value or p-value range?

Use the following information for questions: In the General Social Survey, respondents were asked "Do you favor or oppose the death penalty for persons convicted of murder?" A two-way table summarizing the results for 1447 respondents, by gender, is shown below: -If the null hypothesis of equal proportions of "Favor" responses for males and females were true, what is the expected number of females in the sample who would favor the death penalty?

Use the following information for questions: The table below shows the responses from a sample of 680 people in the General Social Survey to the question, "Do you sometimes drink more than you think you should?" -If the null hypothesis (that there is no association between gender and drinking more than one should) were true, what is the expected number of female respondents who drink more than they should?

Use the following information for questions: In the General Social Survey, respondents were asked what they thought was most important to get ahead: hard work, lucky breaks, or both. Minitab output for 1026 respondents, by gender, is shown below: -At a significance level of 0.05, what is the conclusion?

Use the following information for questions: In the General Social Survey, respondents were asked "If your party nominated a woman for President, would you vote for her if she were qualified for the job?" A two-way table summarizing the results for 953 respondents, by gender, is shown below: -At a significance level of 0.05, what is your conclusion?

Use the following information for questions: In the General Social Survey, respondents were asked "If your party nominated a woman for President, would you vote for her if she were qualified for the job?" A two-way table summarizing the results for 953 respondents, by gender, is shown below: -If the null hypothesis were true, what is the expected number of females in the sample who would give a "No" response to having a female president?

Use the following information for questions: A randomly selected group 78 seniors is asked about their plans after graduation. Is there a relationship between the gender of the students and what they plan to do when they graduate from college? SPSS was used to analyze the data. Part of the output is shown below: -What percentage of male students plan to take a year off?

Use the following information for questions: In the General Social Survey, respondents were asked "Do you favor or oppose the death penalty for persons convicted of murder?" A two-way table summarizing the results for 1447 respondents, by gender, is shown below: -At a significance level of 0.05, what is your conclusion?

Use the following information for questions: In the General Social Survey, respondents were asked, "Do you agree with the following statement? "In spite of what some people say, the lot (situation/condition) of the average man is getting worse, not better." The results, for 989 respondents by gender, are shown below. -The chi-square test statistic = 10.09. What is the p-value or p-value range?

Use the following information for questions: A marketing research group shows three different television advertisements for the same product to each of sixty people to see if the ads are equally effective or not. Each participant is asked which of the three advertisements they believe is most effective. The following table summarizes the counts of how many people found each advertisement to be the most effective. -What is an appropriate null hypothesis for this study?

A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French, Political Science, Undeclared, or Other). What are the degrees of freedom for the chi-square statistic?

Use the following information for questions: The table below shows the opinions of 908 respondents in the General Social Survey to the question "Do you believe there is life after death?" -If the null hypothesis (that there is no association between gender and believing in life after death) were true, what is the expected number of female respondents who believe in life after death?

Use the following information for questions: A gambler wanted to test whether or not a die was fair. He rolled the die 180 times and got the results shown below. For example, the number "1" appeared on 40 rolls. -What are the degrees of freedom for the chi-square goodness of fit statistic?

Which of the following gives statistically significant results at the 0.05 level of significance?

A sociologist uses a z-test to examine the difference between the proportions of men and women opposed to capital punishment. The value of the z-statistic is z = 4. Suppose the sociologist had instead used a chi-square test to analyze the data. What would be the value of the chi-square statistic?