Angioplasty is a medical procedure in which an obstructed blood vessel is widened. In some cases, a wire mesh tube, called a stent, is placed in the vessel to help it remain open. The article "Long-term Outcomes of Patients Receiving Drug-eluting Stents" (A. Philpott, D. Southern, et al., Canadian Medical Association Journal, 2009:167-174) presents the results of a study comparing the effectiveness of a bare metal stent with one that that has been coated with a drug designed to prevent reblocking of the vessel. A total of 5320 patients received bare metal stents, and of these, 841 needed treatment for reblocking within a year. A total of 1120 received drug coated stents, and 134 of them required treatment within a year.
a. Find a 98% confidence interval for the differences between the proportions for drug coated stents and bare metal stents.
b. Suppose that additional patients are to be treated in order to increase the precision of the confidence interval. Three sampling plans are being considered. In the first plan, 1000 additional patients will be treated with bare metal stents. In the second plan, 500 additional patients will be treated with drug coated stents. In the third plan, 500 additional patients will be treated with bare metal stents and 250 additional patients will be treated with drug coated stents. Which plan is most likely to provide the greatest increase in the precision of the confidence interval? Explain.