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.

Winner 70 71 79 71 74 79 73 74 Runner-Up 71 73 74 69 69 74 68 73

a. A well-known theory is that winning candidates are taller than the corresponding losing candidates. Use a 0.05 significance level to test that theory. Does height appear to be an important factor in winning an election?

A. Yes, because the null hypothesis is rejected.

B. No, because the null hypothesis is not rejected.

C. Yes, because the null hypothesis is not rejected.

D. No, because the null hypothesis is rejected.

B.If you plan to test the claim in part (a) by using a confidence interval, what confidence level should be used?

A. 10% B. 5% C. 90% D. 95%

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 election?

A. No, because the confidence interval does not include zero.

B. No, because the confidence interval includes zero.

C. Yes, because the confidence interval does not include include zero.

D. Yes, because the confidence interval includes zero.

Explanation / Answer

Part-a

From following results, we reject the null hypothesis as p-valu=0.023<0.05

A. Yes, because the null hypothesis is rejected.

Paired T-Test and CI: Winner, Runner Up

Paired T for Winner - Runner Up

            N   Mean StDev SE Mean

Winner      8 73.88   3.48     1.23

Runner Up   8 71.38   2.45     0.86

Difference 8   2.50   2.93     1.04

95% lower bound for mean difference: 0.54

T-Test of mean difference = 0 (vs > 0): T-Value = 2.42 P-Value = 0.023

Part-b

We will use 90% confidence level as 5% is only one-sided level , so two sided should be 10%

So, option-C is answr

Part-c

From following results 90% confidence interval=(0.5, 4.5)

Part-d

C. Yes, because the confidence interval does not include include zero.

Paired T-Test and CI: Winner, Runner Up

Paired T for Winner - Runner Up

            N Mean StDev SE Mean

Winner      8 73.88   3.48     1.23

Runner Up   8 71.38   2.45     0.86

Difference 8   2.50   2.93     1.04

90% CI for mean difference: (0.54, 4.46)

T-Test of mean difference = 0 (vs 0): T-Value = 2.42 P-Value = 0.046

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