Question

A study of the effectiveness of using extracts of St. John’s Wort in treating depression was reported in the Journal of the American Medical Association in April, 2001. Patients were randomly divided into two groups. Of the 98 patients in group 1 who received St. John’s Wort, 14 were in remission at the end of the study period. Of the 102 patients in group 2 who received a placebo, 5 were in remission at the end of the study period.

We’d like to construct a two-tailed 99% confidence interval for the difference between the proportion of remission in the St. John’s Wort group and that in the placebo group, and interpret it in terms of the problem context.

a. Justify assumptions for your CI.

b. Compute the 99% confidence interval and interpret it:

Now we apply a hypothesis testing.

c. Let p1: proportion of remission in the St. John’s Wort group and p2: proportion of remission in the placebo group. What are the null and alternative hypotheses?

H₀:

H₁:

d. Justify the assumptions before you compute your test statistic and then compute the test statistic.

e. What is the p-value for this test?

f. What would you conclude from this test at 1% level of significance?

Answer 1