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?