To compare the effectiveness of four drugs in relieving postoperative pain, an experiment was done by randomly assigning 195 surgical patients to the drugs under study. Recorded here are the number of patients assigned to each drug and the number of patients who were free of pain for a period of five hours.

(a) Make a 4 × 2 contingency table showing the counts of patients who were free of pain and those who had pain, and test the null hypothesis that all four drugs are equally effective. (Use a = .05.)
(b) Let p1, p2, p3, and p4 denote the population proportions of patients who would be free of pain under the use of drugs 1, 2, 3, and 4, respectively. Calculate a 90% confidence interval for each of these probabilities individually.

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No, of Patients Free of Pain Assigned Drug23 Drug 230 Drug 3 Drug 4 53 47 51 19 29