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 0.01 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. complete parts (a) and (b) below. all measurements are in years. click the icon to view the table of longevities of archbishops and monarchs. use a 0.01 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. h_0: mu < = mu_2 h_1: mu _1> mu_2 h_0: mu_1= mu_2 h_1: mu_1mu_2 the test statistic is . the p-value is . state the conclusion for the test. reject the null hypothesis. there is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. fail to reject the null hypothesis. there is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. fail to reject the null hypothesis. there is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. reject the null hypothesis. there is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. construct a confidence interval suitable for testing the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation