A national fitness chain is considering being a representative for a weight loss program. The company has narrowed the choice of programs down to two options. Before making the selection, the company has asked each weight loss program to submit a random sample of 40 individuals who were on the program for six months. Of particular interest to the fitness chain is whether there is a difference in the standard deviations of weight loss between the two programs. They will choose the program that has the least amount of variability. The following data were obtained from the two programs:

a. State the appropriate null and alternative hypotheses.
b. Using an alpha level equal to 0.10, test whether the two weight loss programs have equal population standard deviations.

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Program A Program B 20.2 lb 7.3 lb Mean Weight Loss St. Deviation Sample Size 17 lb 4.7 lb 40 40