Mingrone et al. reported the results of an experiment on severely obese patients who had diabetes for at least 5 years. Sixty patients were randomly divided into three groups. One group received medical therapy only (control group), a second group received gastric bypass surgery, and a third group received another kind of surgery called biliopancreatic diversion. It was reported that none of the patients assigned to the control group were free from diabetes after 2 years but that 75% of the gastric-bypass group were free of diabetes and 95% of those receiving biliopancreatic diversion were free from diabetes. Assume that 20 patients were assigned to each group.
a. Find the number of people in each group who were free from diabetes after 2 years.
b. Create a two-way table of the data with Control, Gastric, and Bilio across the top.
c. Test the hypothesis that the treatment and freedom from diabetes are independent using a significance level of 0.05.