Question

(2) 120 pts] In a survey of 400 likely voters, 215 responded that they would vote for the incumbent and 185 responded that they would vote for the challenger. Let p denote the fraction of all likely voters who preferred the incumbent at the time of the survey, and let p be the fraction of survey respondents who preferred the incumbent. (a) Use the survey results to estimate p. (b) Use the estimator of the variance of p, p(1 -p)/n, to calculate the standard error of your estimator (c) What is the P-value for the test Ho : p-0.5 versus the alternative H, : pメ0.5? (d) What is vaue for the fest o 0 vrus the allicemalive P05? (e) Why do the results for the previous two parts differ? (f) Did the survey contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey? (g) Construct a 95% confidence interval for p. (h) Construct a 99% confidence interval for p. (i) Why is the interval in part 2h (j) Without doing any further calculations, test the hypothesis Ho : p-0.5 versus wider than the interval in part (2g)? Ha : pメ0.5 at the 5% significance level.

Answer 1

(f) Since the p value of the one sided test is .0668>.05, the evidence is not significant that incumbent was ahead of the challenger.

A/ her* ST み: PFY..waraan :n