Exam 15: More About Inference for Categorical Variables

Use the following information for questions: Is there a relationship between the color of one's eyes and the comparative lengths of one's index and ring fingers? Students were asked "which finger is longer: your index finger or your ring finger? Or are they the same?" They also reported the color of their eyes (blue, brown, green, or hazel). The analysis of the results is given below. -What are the degrees of freedom for this test?

Use the following information for questions: A student wants to test a claim made by a pizza company. The claim is that the proportion of students whose favorite pizza is pepperoni is 40%, vegetarian is 40%, and all others is 20%. The student takes a random sample of 100 students, and obtained the following results. -If the null hypothesis were true, what are the expected numbers of students in the sample whose favorite pizza is pepperoni, vegetarian, or other?

Which of the following gives statistically significant results?

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?" -Are the results statistically significant at α = 0.05?

Use the following information for questions: At entrance C of the football stadium there are 3 swing gates for the spectators. On football Saturday, two high school students sit at this entrance and count the number of people who enter through each of the swing gates for an hour. On Monday, during their statistics class, they wish to determine if the percentages of people who use each of the three gates on football Saturday are equal. The data they collected during the hour on football Saturday is shown below. -What is the value of the chi-square goodness of fit statistic?

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. -What are the null and alternative hypotheses?

Which of the following gives statistically significant results at the 0.01 level of significance?

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?" Minitab output for 953 respondents, by race, is shown below: -What is the alternative hypothesis for this situation?

Use the following information for questions: A group of 3^rd grade students is given a craft project to take home. Half of the children received an instruction sheet with the project that included photos of examples. The other half of the children were just given general (verbal) instructions from the teacher. At the end of the project the children were asked if they enjoyed doing the project. -Are the results statistically significant at α = 0.05?

Use the following information for questions: At entrance C of the football stadium there are 3 swing gates for the spectators. On football Saturday, two high school students sit at this entrance and count the number of people who enter through each of the swing gates for an hour. On Monday, during their statistics class, they wish to determine if the percentages of people who use each of the three gates on football Saturday are equal. The data they collected during the hour on football Saturday is shown below. -What is the p-value or p-value range?

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 male 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: -What is the alternative hypothesis for this situation?

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. -State the null hypothesis and alternative hypotheses.

Which one of the following is NOT true about the table of expected counts for a chi-square test?

Use the following information for questions: A researcher conducted a study on college students to see if there was a link between gender and how often they have cheated on an exam. She asked two questions on a survey: (1) What is your gender? Male ___ Female ___ (2) How many times have you cheated on an exam while in college? Never __ 1 or 2 times ___ 3 or more times ___ A two-way table of observed counts follows: -Considering the researcher's objectives, what is the appropriate null hypothesis to test?

A chi-square statistic was computed for a two-way table having 1 degree of freedom. The value of the statistic was 6.00. What is the p-value or p-value range?

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 percentage of female students think it is easier to make friends with a girl?

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: -At a significance level of 0.10, what is the conclusion?

Use the following information for questions: A researcher conducted a study on college students to see if there was a link between gender and how often they have cheated on an exam. She asked two questions on a survey: (1) What is your gender? Male ___ Female ___ (2) How many times have you cheated on an exam while in college? Never __ 1 or 2 times ___ 3 or more times ___ A two-way table of observed counts follows: -How many female students would you expect to have cheated once or twice if the null hypothesis were true?

Use the following information for questions: A student wants to test a claim made by a pizza company. The claim is that the proportion of students whose favorite pizza is pepperoni is 40%, vegetarian is 40%, and all others is 20%. The student takes a random sample of 100 students, and obtained the following results. -What are the null and alternative hypotheses for a chi-square goodness of fit test?