Which diet is best? A fairly recent article in the Journal of the American Medical Association (Dansinger, Griffith, Gleason, et al., 2005) reported on a randomized, comparative experiment in which 160 subjects were randomly assigned to one of four popular diet plans: Atkins, Ornish, Weight Watchers, and Zone (40 subjects per diet). These subjects were recruited through newspaper and television advertisements in the greater Boston area; all were overweight or obese with body mass index values between 27 and 42. Data for the 93 subjects who completed the 12-month study are in data file Diets2. The file contains which diet the subject was on and the weight loss in kilograms (positive values indicate weight loss and negative values indicate weight gain).
a. Identify the explanatory variable and the response variable in this study.
b. What are the observational units in this study?
c. State, in words or symbols, the null and alternative hypotheses.
d. Put the data in the Multiple Means applet and describe what the dotplots tell us about the effectiveness of the four diet plans in aiding weight loss.

e. Using the Multiple Means applet find and report the value of a statistic that summarizes the discrepancies between the four diet plans. What is this statistic called?
f. Using a simulation-based approach, test whether there is evidence of an association between weight loss and diet. Be sure to report a p-value.

g. Based on the p-value reported in part (f), state an appropriate conclusion in the context of the study. Be sure to comment on statistical significance, causation, and generalization along with how you are making your decision.