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2. In a survey of 400 likely voters, 2'15 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 f5 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 f), (1 3), to calculate the standard error of your estimator. c. What is the p-value for the test of H0 :p = 0.5 vs. H1 :p 75 0.5. d. What is the p-value for the test of H0 :p = 0.5 vs. H1 :p > 0.5. e. Why do the results from (c) and (d) differ? f. Did the survey contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey? Explain