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 12.8.
TABLE 12.8
A Summary of the Results of a TV Viewership Study

a. Let P1, p2, p3 and p4 be the proportions of all viewers in each age group who watch the station's 11 P.M. news. If these proportions are equal, then whether a viewer watches the station's 11 P.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.

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Watch 11 P.M. News? Yes No Total Age Group 18 or Less 19 to 35 36 to 54 55 or Older 37 213 250 48 202 250 56 194 250 Total 214 786 1,000 73 250