A television station wishes to study the relationship betweenviewership of its 11 p.m. news program and viewer age (18 years orless, 19 to 35, 36 to 54, 55 or older). A sample of 250 televisionviewers in each age group is randomly selected, and the number whowatch the station’s 11 p.m. news is found for each sample. Theresults are given in the table below. Age Group Watch 11 p.m. News?18 or less 19 to 35 36 to 54 55 or Older Total Yes 42 57 61 82 242No 208 193 189 168 758 Total 250 250 250 250 1,000 (a) Let p1, p2,p3, and p4 be the proportions of all viewers in each age group whowatch the station’s 11 p.m. news. If these proportions are equal,then whether a viewer watches the station’s 11 p.m. news isindependent of the viewer’s age group. Therefore, we can test thenull hypothesis H0 that p1, p2, p3, and p4 are equal by carryingout a chi-square test for independence. Perform this test bysetting α = .05. (Round your answer to 3 decimal places.) χ2χ2 = so(Click to select)Do not rejectReject H0: independence (b) Compute a95 percent confidence interval for the difference between p1 andp4. (Round your answers to 3 decimal places. Negative amountsshould be indicated by a minus sign.) 95% CI: [ , ]
