To see if treatment with St John\'s wort improves chances of remission (improvem

Question

To see if treatment with St John's wort improves chances of remission (improvement) for patients suffering from severe depression, patients were divided into two groups, one receiving St John's wort (sample 1), the other receiving a placebo. The results were examined as follows, where X = number in remission in the group (assume that sample sizes are big enough to justify a large-sample normal approximation approach) Test and Confidence Interval for Two Proportions Estimate for p(1) = p(2): 0.0352141 95% CI for p(1) = p(2): (-0.0545156, 0.124944) Test for p(1) = p(2) - 0 (vs > 0): Z = 0.77 P-Value = 0.222 I) The probability value of 0.222 tells us that there is about a 77.8% chance that St John's wort is in fact effective versus placebo. II) We may say, with 95% confidence, that the proportion in remission for those using St John's wort is 5.5% to 12.5% higher than the similar proportion for those taking placebo. III) A type 1 error would be committed if we decided that St John's wort was effective (versus placebo), when in fact it is not. A) I and II are true B) I and III are true C) II and III are true D) One statement or none are true E) All are true

Explanation / Answer

Answer (E) All are true.

Reason 1st, because a p-value of 0.222 indicates z-value = 0.77 which indicates that there is 77% (approx) chance that p1 (st. John's wort) is greater than or more effective that p2 (placebo)

2nd, 95% confidence interval is -0.0545 to 0.125 i.e 5.5% to 12.5% for p1 > p2.

3rd, a type 1 error is rejecting a null hypothesis when it is actually true.

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