4. In a survey of 400 likely voters, 214 responded that they would vote for the incumbent and 186 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. Using the survey results, the estimated value of pis[ (Round your response to four decimal places.) Using (1-P)/n as the estimator of the variance of p, the standard error of the estimator is response to four decimal places.) The p-value for the test Ho: p=0.5 versus H₁: p*0.5 is (Round your (Round your response to three decimal places.) (Round your response to three decimal places.) The p-value for the test Ho: p=0.5 versus H₁: p>0.5 is Why do the p-values for Ho: p=0.5 versus H₁: p0.5 and Ho: p=0.5 versus H₁: p>0.5 differ? OA. H: p=0.5 versus H₁: p>0.5 is a one-sided test and the p-value is the area under the standard normal distribution tr the left of the calculated f-statistic. B. Ho: p=0.5 versus H₁: p0.5 is a two-sided test and the p-value is the area in the tails of the standard normal distribution outside the calculated f-statistic. OC. H: p=0.5 versus H₁: p>0.5 is a two-sided test and the p-value is the area in the tails of the standard normal distribution outside the calculated f-statistic. O D. Ho: p=0.5 versus H₁: p0.5 is a one-sided test and the p-value is the area under the standard normal distribution to the right of the calculated f-statistic. Did the survey contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey? A. For the test H: p=0.5 versus H₁: p0.5, we cannot reject the null hypothesis at the 5% significance level. The p-value is larger than 0.05. The test suggests that the survey did not contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey. B. For the test Ho: p=0.5 versus H₁: p*0.5, we can reject the null hypothesis at the 5% significance level. The p-value less than 0.05. The test suggests that the survey contained statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey. C. For the test Ho: p=0.5 versus H₁: p>0.5, we cannot reject the null hypothesis at the 5% significance level. The p-value is larger than 0.05. The test suggests that the survey did not contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey. D. For the test Ho: p=0.5 versus H₁: p>0.5, we can reject the null hypothesis at the 5% significance level. The p-value less than 0.05. The test suggests that the survey contained statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey.