Chapter 9.2, Problem 11BSC

In Exercises 5–20, 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. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n₁ − 1 and n₂ − 1.)

11. BMI We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person’s body mass index (BMI) is computed by dividing weight (kg) by the square of height (m). Given below are the BMI statistics for random samples of females and males taken from Data Set 1 “Body Data” in Appendix B.

a. Use a 0.05 significance level to test the claim that females and males have the same mean BMI.

b. Construct the confidence interval that is appropriate for testing the claim in part (a).

c. Do females and males appear to have the same mean BMI?

Female BMI: n = 10, $\bar{x}$ = 29.10, s = 7.39

Male BMI: n = 80, $\bar{x}$ = 28.38, s = 5.37