Question

A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.01 significance level for both parts.

Men                 Women

μ          μ1                    μ2

n          11                    59

x          97.78°F           97.25°F

s           0.97°F             0.66°F

a. Test the claim that men have a higher mean body temperature than women.

What are the null and alternative​ hypotheses?

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, t, 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. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

C. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

D. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

_____<μ1−μ2<_____ ​(Round to three decimal places as​ needed.)

Answer 1

What are the null and alternative​ hypotheses?

C. H0​: μ1=μ2

H1​: μ1>μ2

The test​ statistic, t, is _____. ​(Round to two decimal places as​ needed.)

Test Statistic :-


t = 1.7387   1.74

The​ P-value is _____. ​(Round to three decimal places as​ needed.)

Using excel to calculate exact P value = 0.043

Reject null hypothesis if P value < level of significance

0.043 > 0.01, fail to reject null hypothesis

State the conclusion for the test.

B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

Confidence interval :-

DF = 11

Lower Limit =
Lower Limit = -0.4168 - 0.417
Upper Limit =
Upper Limit = 1.4768 1.477
Confidence interval is ( -0.417 , 1.477 )

- 0.417 < μ1−μ2 < 1.477