A television station wishes to study the relationship between viewership of its 11 p.m. news program...

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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 orless 19 to 35 36 to 54 55 orOlder Total
Yes 49 52 67 79 247
No 201 198 183 171 753
Total 250 250 250 250 1,000

(a) Let p₁,p₂, p₃, andp₄ be the proportions of all viewers in eachage group who watch the station’s 11 p.m. news. If theseproportions are equal, then whether a viewer watches the station’s11 p.m. news is independent of the viewer’s age group. Therefore,we can test the null hypothesis H₀ thatp₁, p₂,p₃, and p₄ are equal bycarrying out a chi-square test for independence. Perform this testby setting ? = .05. (Round your answer to 3 decimalplaces.)

?2
=
so
H₀: independence

(b) Compute a 95 percent confidence interval forthe difference between p₁ andp₄. (Round your answers to 3 decimalplaces. Negative amounts should be indicated by a minussign.)

95% CI: [ , ]

Answer & Explanation Solved by verified expert

3.9 Ratings (456 Votes)

SolutionaState the hypotheses The first step is tostate the null hypothesis and an alternative hypothesisNull hypothesis p1 p2 p3 p4Alternative hypothesis At least one of the null hypothesisstatements is falseFormulate an analysis plan For this analysisthe significance level is 005 Using See Answer

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		Age Group
Watch 11 p.m. News?	18 orless	19 to 35	36 to 54	55 orOlder	Total
Yes	49	52	67	79	247
No	201	198	183	171	753
Total	250	250	250	250	1,000