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**homalina** 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 H_{0}: p=0.5 vs H_{1}: p > 0.5?

d. What is the p-value for the test H_{0}: p=0.5 vs H_{1}: p not equal to 0.5?

e. Why do the result from c and d differ?

f. Explain if the survey contained statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey?

Please help.

Thanks