Treating depression with St. John’s wort. The Journal of the American Medical Association (Apr. 18, 2001) published a study of the effectiveness of using extracts of the herbal medicine St. John’s wort in treating major depression. In an eight-week randomized, controlled trial, 200 patients diagnosed with major depression were divided into two groups, one of which 1n1 = 982 received St. John’s wort extract while the other 1n2 = 1022 received a placebo (no drug). At the end of the study period, 14 of the St. John’s wort patients were in remission, compared with 5 of the placebo patients.

a. Compute the proportion of the St. John’s wort patients who were in remission.

b. Compute the proportion of the placebo patients who were in remission.

c. If St. John’s wort is effective in treating major depression, then the proportion of St. John’s wort patients in remission will exceed the proportion of placebo patients in remission. At a = .01, is St. John’s wort effective in treating major depression?

d. Repeat part

c, but use a = .10.

e. Explain why the choice of a is critical for this study.