Listed below are the heights of candidates who won elections and the heights of

Question

Listed below are the heights of candidates who won elections and the heights of the candidates with the next highest number of votes. The data are in chronological order, so the corresponding heights from the two lists are matched. a. A well-known theory is that winning candidates are taller than the corresponding losing candidates. Use a 0.05 significance level in test that theory. height appear to be an important factor in winning a election? A. Yes, because the null hypothesis is not rejected. B. Yes, because the null hypothesis is rejected. C. No, because the null hypothesis is rejected. D. No, because the null hypothesis is not rejected. b. If you plan to test the claim in part(a) by using a confidence interval, what confidence level should be used? A. 50% B. 96% C. 5% D. 10% Construct a confidence interval using that level, then interpret the result. (Round to one decimal place as needed.) Based on the confidence interval, does height appear to be an important factor in winning an electron? A. No, because the confidence interval includes zero. B. Yes, because the confidence interval does not include zero. C. Yes, because the confidence interval includes zero. D. No, because the confidence interval does not include zero.

Explanation / Answer

Part-a –Option-C

This is due to the fact that p-value=0.575>0.05

Paired T-Test and CI: Winning, Runner-Up

Paired T for Winning - Runner-Up

            N    Mean StDev SE Mean

Winning     8 71.375 2.134    0.754

Runner-Up   8 71.500 2.204    0.779

Difference 8 -0.125 1.808    0.639

95% lower bound for mean difference: -1.336

T-Test of mean difference = 0 (vs > 0): T-Value = -0.20 P-Value = 0.575

Part-b-Option-B

This is because 0.05 level of significance corresponds to 95% confidencelevel

Part-c : -1.6<µd<1.4

From following output we have

95% CI for difference: (-1.636, 1.386)

Paired T-Test and CI: Winning, Runner-Up

Paired T for Winning - Runner-Up

            N    Mean StDev SE Mean

Winning     8 71.375 2.134    0.754

Runner-Up   8 71.500 2.204    0.779

Difference 8 -0.125 1.808    0.639

95% CI for mean difference: (-1.636, 1.386)

T-Test of mean difference = 0 (vs 0): T-Value = -0.20 P-Value = 0.850

Part-d-Option-A

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