Pain after surgery:In a random sample of53patients undergoing a standard surgical procedure,2required medication for postoperative pain. In a random sample of89patients undergoing a new procedure, only10required pain medication.

(a) Construct a99.5% confidence interval for the difference in the proportions of patients needing pain medication between the old and new procedures. Letp1denote the proportion of patients who had the old procedure needing pain medication and let

p2 denote the proportion of patients who had the new procedure needing pain medication. Use the TI-84 Plus calculator and round the answers to three decimal places.