Experiments and clinical trials with different treatment groups commonly include information about the characteristics of those groups. In a study of four different weight loss programs, each program had 40 subjects. The means and standard deviations of the ages in each group are as follows: Atkins ( years); Zone ( years, s ); Weight Watchers ( years, s years); Ornish ( years, s years). These statistics are listed along with a P-value of 0.41. These results are from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction,” by Dansinger, et al., Journal of the American Medical Association, Vol. 293, No. 1.

a. How many variables are used to categorize the sample data consisting of ages?

b. What specific method is used to find the P-value of 0.41?

c. What does the P-value of 0.41 indicate about the baseline characteristic of age?

d. What would a small P-value (such as 0.001) indicate about the ages, and how would that affect the results of the study?