Chapter 9.2, Problem 5BSC

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.)

5. Regular Coke and Diet Coke Data Set 26 “Cola Weights and Volumes” in Appendix B includes weights (lb) of the contents of cans of Diet Coke (n = 36, $\bar{x}$ = 0.78479 lb, s = 0.00439 lb) and of the contents of cans of regular Coke (n = 36, $\bar{x}$ = 0.81682 lb, s = 0.00751 lb).

a. Use a 0.05 significance level to test the claim that the contents of cans of Diet Coke have weights with a mean that is less than the mean for regular Coke.

b. Construct the confidence interval appropriate for the hypothesis test in part (a).

c. Can you explain why cans of Diet Coke would weigh less than cans of regular Coke?