In a random sample of 50 patients undergoing a standard surgical procedure, 15 required medication for postoperative pain. In a random sample of 90 patients undergoing a new procedure, only 16 required pain medication.

a. Construct a 95% confidence interval for the difference in the proportions of patients needing pain medication between the old and new procedures.

b. A physician claims that the proportion of patients who need pain medication is the same for both procedures. Does the confidence interval contradict this claim?