A television station wishes to study the relationship between viewership of its 11 P. M. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 P. M. news is found for each sample. The results are given in Table 12.7.
a. Let p1, p2, p3, and p4 be the proportions of all viewers in each age group who watch the station’s 11P.M. news. If these proportions are equal, then whether a viewer watches the station’s 11P.M. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H0 that p1, p2, p3, and p4 are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05.
b. Compute a 95 percent confidence interval for the difference between p1 and p4.