13.53 The data in Example 13.1, on body temperature for young adults, was part of a larger set of body temperatures taken on 100 adults at a blood donor center. The data are in the file bodytemp on the website for this book. The Minitab output below shows the results of the “2-sample t” procedure for comparing the body temperatures of males and females.

Sex N Mean StDev SE Mean Female 46 98.102 0.651 0.096 Male 54 97.709 0.762 0.10 Difference 5 mu (Female) 2 mu (Male)

Estimate for difference: 0.393 95% CI for difference: (0.112, 0.673)

T-Test of difference 5 0 (vs not 5): T-Value 5 2.78 P-Value 5 0.007 DF 5 97

a. Give the null and alternative hypotheses using symbols.

b. What is the value of the test statistic t?

c. Identify the numbers that were used to compute the t-statistic, and verify that the reported value is correct.

d. What conclusion would be made using a .05 level of significance?

Write the conclusion in statistical terms and in the context of the problem.