Chapter 9: Inference for Categorical Data

SECTION 9.1 EXERCISES

For Exercises 9.1, 9.2, and 9.3, see pages 531–532; for Exercises 9.4, 9.5, and 9.6, see page 539; for Exercise 9.7, Exercise 9.8, Exercise 9.9 and Exercise 9.10, see page 540; for Exercises 9.11, 9.12, and 9.13, see page 541; and for Exercise 9.14, see page 543.

Question 9.15

9.15 Adult gamers versus teen gamers. In Exercise 8.67 (page 521), you analyzed data from a study that compared adult gamers with teen gamers with respect to the devices on which they play. The study surveyed 1063 adult gamers and 1064 teen gamers. For the adults, 54% played on game consoles (Xbox, PlayStation Wii, etc.), while 89% of the teen gamers played on game consoles. Your analysis in Exercise 8.67 focused on the comparison of two proportions. Use these data to construct a two-way table for analysis.

9.15

Gamer
Consoles	Adult	Teen	Total
Yes	574	489	1063
No	945	119	1064
Total	1519	608

Question 9.16

9.16 Physical education requirements. In Exercise 8.63 (page 520), you analyzed data from a study that included 354 higher education institutions: 225 private and 129 public. Among the private institutions, 60 required a physical education course, while among the public institutions, 101 required a course. Your analysis in that exercise focused on the comparison of two proportions. Use these data to construct a two-way table for analysis.

Question 9.17

9.17 Adult gamers versus teen gamers. Refer to Exercise 9.15. Find the joint distribution, the marginal distributions, and the conditional distributions. Which conditional distribution do you prefer to explain the results of your analysis? Give a reason for your answer.

9.17 27% are adult who play games on consoles, 23% are teens who play games on consoles, 44.4% are adults who don’t play games on consoles, 5.6% are teens who don’t play games on consoles. 71.42% are adults and 28.58% are teen. 49.98% play games on consoles, 50.02% do not. For adult gamers, 37.79% play games on consoles, 62.21% do not. For teen gamers, 80.43% play games on consoles, 19.57% do not. For those who play games on consoles, 54% are adult gamers, 46% are teen gamers. For those who do not play games on consoles, 88.82% are adult gamers, 11.18% are teen gamers. Usage of game consoles by gamer type are probably the most informative. A much higher percent of teen gamers play games on consoles than adult gamers.

Question 9.18

9.18 Physical education requirements. Refer to Exercise 9.16. Find the joint distribution, the marginal distributions, and the conditional distributions. Which conditional distribution do you prefer to explain the results of your analysis? Give a reason for your answer.

Question 9.19

9.19 Adult gamers versus teen gamers. Refer to Exercise 9.15. Find the expected counts.

9.19 The expected counts are 759.14, 303.86, 759.86, 304.14.

Question 9.20

9.20 Physical education requirements. Refer to Exercise 9.16. Find the expected counts.

Question 9.21

9.21 Adult gamers versus teen gamers. Refer to Exercise 9.15. Find the chi-square statistic and the $P$ -value. What do you conclude?

9.21 X² = 315.7770, df = 1, P-value < 0.0001.

Question 9.22

9.22 Physical education requirements. Refer to Exercise 9.16. Find the chi-square statistic and the $P$ -value. What do you conclude?

Question 9.23

9.23 Adult gamers versus teen gamers. Refer to Exercise 9.15. Show that the chi-square statistic that you found in Exercise 9.21 is the square of the $z$ statistic that you found in Exercise 8.68.

9.23 X² = 315.7770 ≈ z² = ( − 17.77)² = 315.7729.

Question 9.24

9.24 Physical education requirements. Refer to Exercise 9.16. Show that the chi-square statistic that you found in Exercise 9.22 is the square of the $z$ statistic that you found in Exercise 8.63.

Question 9.25

haras1

9.25 Sexual harassment in middle and high schools. A nationally representative survey of students in grades 7 to 12 asked about the experience of these students with respect to sexual harassment.⁶ One question asked how many times the student had witnessed sexual harassment in school. The two-way table for this exercise is given in Figure 9.8. Use the figure to find the joint distribution, the two marginal distributions, and the conditional distributions. Which conditional distribution do you prefer to explain the results of your analysis? Give a reason for your answer.

9.25 More and Boys: 37.23%; More and Girls: 34.13%. Never and Boys: 5.39%; Never and Girls: 7.12%. Once and Boys: 6.36%; Once and Girls: 9.77%. 48.98% are boys, 51.02% are girls. 71.36% have witnessed it more than once, 16.12% have witnessed it once, and 12.51% have never witnessed it. For boys: 76.01% have witnessed it more than once, 12.98% have witnessed it once, and 11.01% have never witnessed it. For girls: 66.90% have witnessed it more than once, 19.14% have witnessed it once, and 13.96% have never witnessed it. For those witnessing sexual harassment more than once: 52.17% are boys, 47.83% are girls. For those witnessing sexual harassment once: 39.43% are boys, 60.57% are girls. For those never witnessing sexual harassment: 43.09% are boys, 56.91% are girls. The distribution of times by sex are probably the most informative, showing that boys tend to say they have witnessed sexual harassment slightly more than girls, with boys having 10% higher in the More category than the girls.

Question 9.26

rdc

9.26 Remote deposit capture. The Federal Reserve has called remote deposit capture (RDC) “the most important development the [U.S.] banking industry has seen in years.’’ This service allows users to scan checks and to transmit the scanned images to a bank for posting.⁷ In its annual survey of community banks, the American Bankers Association asked banks whether or not they offered this service.⁸ The two-way table for this exercise is given in Figure 9.9. Use the figure to find the joint distribution, the two marginal distributions, and the conditional distributions. Which conditional distribution do you prefer to explain the results of your analysis? Give a reason for your answer.

Question 9.27

haras1

9.27 Sexual harassment in middle and high schools. Refer to Exercise 9.25. Use the output in Figure 9.8 to find the chi-square statistic, the degrees of freedom, and the $P$ value. What do you conclude from this analysis?

9.27 X² = 20.822, df = 2, P-value < 0.0001.

Question 9.28

rdc

9.28 Remote deposit capture. Refer to Exercise 9.26. Use the output in Figure 9.9 to find the chi-square statistic, the degrees of freedom, and the $P$ value. What do you conclude from this analysis?

Page 545

Figure 9.8: FIGURE 9.8 Computer output, Exercises 9.25 and 9.27.

Figure 9.9: FIGURE 9.9 Computer output, Exercises 9.26 and 9.28.