Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation. Treat the values as simple random samples from larger populations. Use a 0.05 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. All measurements are in years. Archbishops: 18, 15, 18, 15, 17, 1, 15, 17, 10, 13, 14, 10, 14, 15, 14, 11, 18, 18, 8, 16, 11, 2, 16, 18
Monarchs: 17, 20, 14, 11, 16, 19, 20, 18, 13, 20, 17, 18
a. Use a 0.05 significance level, and test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs.
b. The test statistic is . (Round to two decimal places as needed.)
c. The P-value is . (Round to two decimal places as needed.)
d. State the conclusion for the test.
A. Reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.
B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.
C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.
D. Reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.
e. Construct a confidence interval suitable for testing the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. (Round to three decimal places as needed.)
f. Does the confidence interval support the conclusion of the test?
because the confidence interval contains .