The U.S. Federal Trade Commission assesses fines and other penalties against weight-loss clinics that make unsupported or misleading claims about the effectiveness of their programs. Brochures from two weight-loss clinics both advertise "statistical evidence" about the effectiveness of their programs. Clinic A claims that the mean weight loss during the first month is 15 pounds; Clinic B claims a median weight loss of 10 pounds.
a. Assuming the statistics are accurately calculated, which clinic would you recommend if you had no other information? Why?
b. Upon further research, the median and standard deviation for Clinic A are found to be 10 pounds and 20 pounds, respectively, while the mean and standard deviation for Clinic B are found to be 10 and 5 pounds, respectively. Both are based on samples of more than 100 clients. Describe the two clinics' weight-loss distributions as completely as possible given this additional information. What would you recommend to a prospective client now? Why?
c. Note that nothing has been said about how the sample of clients upon which the statistics are based was selected. What additional information would be important regarding the sampling techniques employed by the clinics?