Chapter 9, Problem 72SE

Body Temperature The body temperatures of 65 men and 65 women were compared. The results of a hypothesis test are shown. Assume the conditions for using a $t\text{-test}$ are satisfied. (Source: Body Temperature, accessed via StatCrunch. Owner: StatCrunch featured.)

a. Why was a two-sample $t\text{-test}$ used instead of a paired $t\text{-test}$ ?

b. Which sample mean is larger? How do you know?

c. Write the conclusion for the hypothesis test.

Two sample T hypothesis test:

${\text{μ}}_1$ : Mean of Body Temp where Gender $=$ “Female”

${\text{μ}}_2$ : Mean of Body Temp where Gender $=$ “Male”

${\text{μ}}_1-{\text{μ}}_2$ : Difference Between two means

${\text{H}}_{\text{0}}:{\text{μ}}_1-{\text{μ}}_2=0$

${\text{H}}_{\text{A}}:{\text{μ}}_1-{\text{μ}}_2\ne 0$

(without pooled variances)

Hypothesis test results: