Question

8. 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.

Archbishops	18	15	16	15	15	2	14	17	10	15	12	13
	15	14	15	13	17	18	10	17	11	0	23	13
Monarchs	18	19	13	13	17	15	20	16	15	14	17	16

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.

a. H0: µ1≠µ2

H1: µ1>µ2

b. H0: µ1=µ2

H1: µ1≠µ2

c. H0: µ1=µ2

H1: µ1<µ2

d.H0: µ1≤µ2

H1: µ1>µ2

The test statistic is ____

​(Round to two decimal places as​ needed.)

The​ P-value is ____

(Round to three decimal places as​ needed.)

State the conclusion for the test.

A.Fail to reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

B.Reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

C.Reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

D.Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

b. Construct a confidence interval suitable for testing the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation.

___<µ1-µ2<____

​(Round to three decimal places as​ needed.)

Does the confidence interval support the conclusion of the​ test?

(No,Yes,) because the confidence interval contains (only negative values., zero, only positive values.)

Answer 1

	Archbishops ( X )		Monarchs ( Y )
	18	18.7775	18	3.6737
	15	1.7777	19	8.5071
	16	5.4443	13	9.5067
	15	1.7777	13	9.5067
	15	1.7777	17	0.8403
	2	136.1119	15	1.1735
	14	0.1111	20	15.3405
	17	11.1109	16	0.0069
	10	13.4447	15	1.1735
	15	1.7777	14	4.3401
	12	2.7779	17	0.8403
	13	0.4445	16	0.0069
	15	1.7777
	14	0.1111
	15	1.7777
	13	0.4445
	17	11.1109
	18	18.7775
	10	13.4447
	17	11.1109
	11	7.1113
	0	186.7787
	23	87.1105
	13	0.4445
Total	328	535.3336	193	54.9162

Mean

Standard deviation

Mean

Standard deviation

c. H0: µ1=µ2

H1: µ1<µ2

Test Statistic :-


t = -2.0528   - 2.05

Test Criteria :-
Reject null hypothesis if


DF = 33


Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 2.0528 ) = 0.024
Reject null hypothesis if P value < level of significance
P - value = 0.024 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

C.Reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

Confidence interval :-



Lower Limit =
Lower Limit = -4.8117
Upper Limit =
Upper Limit = -0.0215
95% Confidence interval is ( -4.8117 , -0.0215 )

(Yes,) because the confidence interval contains (only negative values.)