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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? Yes 18 or less 19 to 35 36 to 54 Older Total 43 53 56 81 233 No 207 197 194 169 767 Total 250 250 250 250 1,000 (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 H, that p1, P2. P3, and p4 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 = HO: independence so (b) Compute a 95 percent confidence interval for the difference between Pi and P4. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) 95% Cl: [ 1

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? Yes 18 or less 19 to 35 36 to 54 Older Total 43 53 56 81 233 No 207 197 194 169 767 Total 250 250 250 250 1,000 (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 H, that p1, P2. P3, and p4 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 = HO: independence so (b) Compute a 95 percent confidence interval for the difference between Pi and P4. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) 95% Cl: [ 1

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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ch 15 end. 7: 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.
 

 

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 18 or less 11 p.m. News? Yes 19 to 35 36 to 54 Older Total 43 53 56 81 233 No 207 197 194 169 767 Total 250 250 250 250 1,000 (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 Pą 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 = HO: independence so (b) Compute a 95 percent confidence interval for the difference between pą and p4. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) 95% CI: [
Transcribed Image Text: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 18 or less 11 p.m. News? Yes 19 to 35 36 to 54 Older Total 43 53 56 81 233 No 207 197 194 169 767 Total 250 250 250 250 1,000 (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 Pą 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 = HO: independence so (b) Compute a 95 percent confidence interval for the difference between pą and p4. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) 95% CI: [
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