?In Exercises 5–20, assume that the two samples are independent simple random samples

Chapter 9, Problem 5

(choose chapter or problem)

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 \(n_{1}-1\) and \(n_{2}-1\).)

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?

Text Transcription:

n_1-1

n_2-1

n=36

\barx=0.78479

s=0.00439

\barx=0.81682

s=0.00751