Listed below are the numbers of years that archbishops and monarchs in a certain

Question

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. Complete parts (a) and (b) below. All measurements are in years. calculate p-value? test statistic ? u1-u2?

Archbishops

                     17 17 14 16 15 3 18 17 12 12 14 13

                    16 12 12 15 14 15 7 15 12 1 21 19

Monarchs    13 16 15 13 19 15 20 17 16 14 20 17

Explanation / Answer

The above problem can be solved in R studio using the following command.

Archibishops<-c(17,7,14,16,15,3,18,17,12,12,14,13,16,12,12,15,14,15,7,15,12,1,21,19)
Monarchs<-c(13,16,15,13,19,15,20,17,16,14,20,17)
t.test(Archibishops,Monarchs)

Output:

Welch Two Sample t-test

data: Archibishops and Monarchs
t = -2.5409, df = 33.889,
p-value = 0.0158
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-5.4746990 -0.6086344
sample estimates:
mean of x mean of y
13.20833 16.25000 .

Therefore, here

test stastic=-2.5409

p-value=0.0158.

Since pvalue<0.05,H0 is rejected.

Which means there is enough evidence to support the claim.

The interval of difference in means is ( -5.4746990 -0.6086344).

Please give a THUMBS UP!!!

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