Chapter 8.4, Problem 9BSC

Testing Claims About Variation. In Exercises 5-16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population.

9. Cola Cans A random sample of 20 aluminum cola cans with thickness 0.0109 in. is selected and the axial loads are measured and the standard deviation is 18.6 lb. The axial load is the pressure applied to the top that causes the can to crush. Use a 0.05 significance level to test the claim that cans with thickness 0.0109 in. have axial loads with the same standard deviation as the axial loads of cans that are 0.0111 in. thick. The thicker cans have axial loads with a standard deviation of 27.8 lb (based on Data Set 30 “Aluminum Cans” in Appendix B). Does the thickness of the cans appear to affect the variation of the axial loads?