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.
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?
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Test of p = 0.25 vs p > 0.25
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Sample X
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N
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Sample p
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Z-Value
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P-Value
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1 146
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400
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0.365000
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5.31
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0.000
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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.
d. Do you think that the result of the station's survey has practical importance? Why or why not?