Question

Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is more effective for women than for men. We want to collect data to show that the new drug is more effective for men. Let p1=proportion of all men who catch a cold , after taking the new drug p2=proportion of all women who catch a cold, after taking the new drug The null hypothesis states Ho: p1-p2=0 (or p1=p2, equivalently)

1. What is the alternative hypothesis? (pick one and clarify whether this a left tail test, a right tail test or a two-sided test).

A. Ha : p1-p2 > 0

B. Ha: p1-p2 < 0

C. Ha: p1-p2≠0

We choose a random sample of 100 women and 200 men from a population of 100,000 volunteers. At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. We calculated the test statistic (z-score) , and we found that it is equal to 2.13 (i.e. z=2.13) .

2. Calculate the p-value for this test (use Table A).

3. Based on the p-value, can we conclude that the drug is more effective for men than for women? (Use a 0.05 level of significance). Explain your answer.

Answer 1