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Last year, television station WXYZ's share of the 11 P.M. news audience was approximately equal to, but no greater than, 25 percent. The station's management believes that the current audience share is higher than last year's 25 percent share. In an attempt to substantiate this belief, the station surveyed a random sample of 400 11 PM news viewers and found that 146 watched WXYZ. (a) Let p be the current proportion of all 11 P.M. news viewers who watch WXYZ. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that the current audience share for WXYZ is higher than last year's 25 percent share. HO: P versus Ha: p

Last year, television station WXYZ's share of the 11 P.M. news audience was approximately equal to, but no greater than, 25 percent. The station's management believes that the current audience share is higher than last year's 25 percent share. In an attempt to substantiate this belief, the station surveyed a random sample of 400 11 PM news viewers and found that 146 watched WXYZ. (a) Let p be the current proportion of all 11 P.M. news viewers who watch WXYZ. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that the current audience share for WXYZ is higher than last year's 25 percent share. HO: P versus Ha: p

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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Last year, television station WXYZ's share of the 11 P.M. news audience was approximately equal to, but no greater than, 25 percent The station's management believes that the current audience share is higher than last year's 25 percent share. In an attempt to substantiate this belief, the station surveyed a random sample of 400 11 P.M. news viewers and found that 146 watched WXYZ. (a) Let p be the current proportion of all 11 P.M. news viewers who watch WXYZ. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that the current audience share for WXYZ is higher than last year's 25 percent share. HO: P versus Ha: p
Transcribed Image Text:Last year, television station WXYZ's share of the 11 P.M. news audience was approximately equal to, but no greater than, 25 percent The station's management believes that the current audience share is higher than last year's 25 percent share. In an attempt to substantiate this belief, the station surveyed a random sample of 400 11 P.M. news viewers and found that 146 watched WXYZ. (a) Let p be the current proportion of all 11 P.M. news viewers who watch WXYZ. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that the current audience share for WXYZ is higher than last year's 25 percent share. HO: P versus Ha: p
(b) Use critical values and the following MINITAB output to test the hypotheses you set up in part a at the 10, 05, 01, and .001 levels of significance. How much evidence is there that the current audience share is higher than last year's 25 percent share? (Round your p answer to 3 decimal places and the z values to 2 decimal places.) Test of p= 0.25 vs p > 0.25 Sample N X 146 Sample p 0.365000 1 Z-Value 400 P-Value 0.000 5.31 Z 2.001 Reject HO at a- evidence (c) Find the p-value for the hypothesis test in part b. Use the p-value to carry out the test by setting a equal to 10, 05, 01, and 001. Interpret your results. p-value is 001; HO at all given values of a (d) Do you think that the result of the station's survey has practical importance? (Round the sample proportion to 3 decimal places.) The sample proportion of than 25 is significantly
Transcribed Image Text:(b) Use critical values and the following MINITAB output to test the hypotheses you set up in part a at the 10, 05, 01, and .001 levels of significance. How much evidence is there that the current audience share is higher than last year's 25 percent share? (Round your p answer to 3 decimal places and the z values to 2 decimal places.) Test of p= 0.25 vs p > 0.25 Sample N X 146 Sample p 0.365000 1 Z-Value 400 P-Value 0.000 5.31 Z 2.001 Reject HO at a- evidence (c) Find the p-value for the hypothesis test in part b. Use the p-value to carry out the test by setting a equal to 10, 05, 01, and 001. Interpret your results. p-value is 001; HO at all given values of a (d) Do you think that the result of the station's survey has practical importance? (Round the sample proportion to 3 decimal places.) The sample proportion of than 25 is significantly
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