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 H0: p=0.5 vs H1: p > 0.5?
d. What is the p-value for the test H0: p=0.5 vs H1: 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?