Spertus et al. (A-20) performed a randomized single blind study for subjects with stable coronary artery disease. They randomized subjects into two treatment groups. The first group had current angina medications optimized, and the second group was tapered off existing medications and then started on long-acting diltiazem at 180 mg/day. The researchers performed several tests to determine if there were significant differences in the two treatment groups at baseline. One of the characteristics of interest was the difference in the percentages of subjects who had reported a history of congestive heart failure. In the group where current medications were optimized, 16 of 49 subjects reported a history of congestive heart failure. In the subjects placed on the diltiazem, 12 of the 51 subjects reported a history of congestive heart failure. State the assumptions that you think are necessary and construct a 95 percent confidence interval for the difference between the proportions of those reporting congestive heart failure within the two populations from which we presume these treatment groups to have been selected.