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 the table below. Age Group Watch 55 or 11 p.m. News? 18 or less 19 to 35 36 to 54 Older Total Yes 38 59 69 75 241 No 212 191 181 175 759 Total 250 250 250 250 1, 900 (a) Let P1, P2, P3, and pa 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 He that P1, P2. P3, and pa are equal by carrying out a chi-square test for independence. Perform this test by setting a = .05. (Round your answer to 3 decimal places.) X 2 = SO HO: independence(b) Compute a 95 percent confidence interval for the difference between p; and p,. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) oewaf [P |