Question

8. 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 0.05 significance level for both parts.

	Men	Women
μ	μ1	μ2
n	11	59
x	97.64 F	97.32 F
s	0.94 F	0.72 F

a. what are the null and alternative hyphotesis?

b. what is the test statistic? (two decimal)

c. what is the p-value (three decimal)

d. State the conclusion for the test

e. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean (three decimal)

f. Does the confidence interval support the conclusion found with the hypothesis test?

Answer 1

a) To test null hypothesis against alternative hypothesis

b) The test statistic can be written as

which under H₀ follows a t distribution with df

where

We reject H₀ at 5% level of significance if p-value < 0.05

b) Now,

associated degrees of freedom

The value of the test statistic

c) and p-value

d) Since p-value > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that mean body temperatures of men and women are not significantly different.

e) a 95% confidence interval for difference between mean body temperatures of men and women

f) Since the confidence interval includes 0, so we fail to reject H₀ at 5% level of significance and we can conclude that mean body temperatures of men and women are not significantly different.