In a survey of 400 likely voters, 216 responded that they would vote for the incumbent and 184 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 p is(Round your response to four decimal places.)Using p(1- p)/n as the estimator of the variance of p, the standard error of the estimator is(Round your response to four decimal places.)The p-value for the test Ho: p= 0.5 versus H1: p#0.5 is(Round your response to three decimal places.)The p-value for the test H,: p= 0.5 versus H1: p> 0.5 is(Round your response to three decimal places.).Why do the p-values for H,: p= 0.5 versus H1: p#0.5 and Ho: p= 0.5 versus H,: p>0.5 differ?A. H: p= 0.5 versus H4: p>0.5 is a one-sided test and the p-value is the area under the standard normal distribution to the left of the calculated t-statistic.B. Ho: p=0.5 versus H: 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 t-statistic.O C. Ho: 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 to the right of the calculated t-statistic.O D. H,: p=0.5 versus H4: 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 t-statistic.Did the survey contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey?O A. For the test H,: p= 0.5 versus H1: p> 0.5, we can reject the null hypothesis at the 5% significance level. The p-value is less than 0.05. The test suggests that the survey contained statistically significant evidence that the incumbent wasahead of the challenger at the time of the survey.O B. For the test Ho:p=0.5 versus H: p#0.5, we can reject the null hypothesis at the 5% significance level. The p-value is less than 0.05. The test suggests that the survey contained statistically significant evidence that the incumbent wasahead of the challenger at the time of the survey.O C. For the test H,: 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 theincumbent was ahead of the challenger at the time of the survey.O D. For the test Ho:p=0.5 versus Hq: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 theincumbent was ahead of the challenger at the time of the survey.Click to select your answer(s).SpreadsheetO Time Remaining: 00:28:39Next吕0F3escF1F2O00F4F5F6F7F8F9F10F11F12!@$4&*2678deleteQERTYU{}tabenterASFGHJKLcaps lockreturn+ ||# 3

Name: In a survey of 400 likely voters, 216 responded that they would vote
Uploaded: 2024-03-20T07:06:27.000Z
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Description: In a survey of 400 likely voters, 216 responded that they would vote for the incumbent and 184 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,an