In a survey of 400 likely voters, 216 responded that they would vote for the inc

Question

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-D)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 Ho, p = 0.5 versus H1: p> 0.5 is 1. (Round your response to three decimal places.) Why do the p-values for Ho·p= 0.5 versus HI : p0.5 and Ho: p= 0.5 versus H1 : p > 0.5 differ? A. 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 t-statistic. B. Ho: p= 0.5 versus HI : 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. ° C. tlgi 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 left of the calculated t-statistic 0 D. Ho: 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 t-statistic. Did the survey contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey? ( A. B. C. 0 D. For the test Ho: p = 0.5 versus HI : p> 0.5, we cannot reject the null hypothesis at the 5% significance level because the p-value is greater 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 For the test Ho: p= 0.5 versus H1 : p#0.5, we can reject the null hypothesis at the 5% significance level because the p-value is greater 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 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 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. For the test Hn·p= 0.5 versus H1 : p> 0.5, we can reject the null hypothesis at the 5% significance level because the p-value is greater than 0.05. The test survey

Explanation / Answer

Answer to the question is as follows:

The estimated value of p^ = x/n = 216/400 = .54

The standard error = sqrt(p^*(1-p^)/n) = sqrt((.54*.46)/400) = .025

Lets calculate test statistic = (p^ -p )/SE = (.54-.50)/.025 = 1.6

The p-value for the test Ho: p=.5 vs. H1: p!=.5 is .11

The p-value for the test Ho: p=.5 vs. H1: p>.50 is 0.055

1. A is correct. Ho: p =.5 and H1:p!=.5 is a 2 sided test and p-value is the area under std normal dist outside +/- calculated t sttistic

2. A is correct. We got a p-value greater than .05 and hence we can't reject Ho.

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