A survey is conducted using 1000 registered voters, who are
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A survey is conducted using 1000 registered voters, who are asked to choose between candidate A and candidate B. Let p d
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A survey is conducted using 1000 registered voters, who are asked to choose between candidate A and candidate B. Let p denote the fraction of voters in the population who prefer candidate A, and let pn denote the fraction of voters who prefer Candidate B. a. You are interested in the competing hypotheses H0: p = 0.4 vs. H1: p ? 0.4. Suppose that you decide to reject H0 if pn - 0.4 7 0.01. Then i. What is the size of this test? ii. Compute the power of this test if p = 0.45. b. In the survey, pn = 0.44. i. Test H0: p = 0.4 vs. H1: p ? 0.4 using a 10% significance level. ii. Test H0: p = 0.4 vs. H1: p 6 0.4 using a 10% significance level. iii. Construct a 90% confidence interval for p. iv. Construct a 99% confidence interval for p. v. Construct a 60% confidence interval for p. c. Suppose the survey is carried out 30 times, using independently selected voters in each survey. For each of these 30 surveys, a 90% confidence interval for p is constructed. i. What is the probability that the true value of p is contained in all 30 of these confidence intervals? ii. How many of these confidence intervals do you expect to contain the true value of p? d. In survey jargon, the
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