Question

Suppose that a group of 800 smokers trying to quit were randomly selected to receive an antidepressant drug or a placebo for six weeks. of the 400 patients who received the antidepressant drug, 141 were not smoking one year later. of the 400 patients who received the placebo, 81 were not smoking one year later. test the claim that antidepressants are effective in helping people to quit smoking at a significance level of α=0.05.

State the null and alternative hypotheses: let p1 be the proportion that were still not smoking from the antidepressant group, and p2 be the proportion that were still not smoking from the placebo group. type either "=", ">", "<", or "not =".

Answer 1

Null Hypothesis (H0): The proportion who quit smoking is the same for antidepressant and placebo groups (p1 = p2).

Alternative Hypothesis (H1): Antidepressant group has a higher proportion who quit (p1 > p2).

The null and alternative hypotheses for testing the claim that antidepressants are effective in helping people quit smoking at a significance level of α=0.05 can be stated as follows:

Null Hypothesis (H0): The proportion of individuals who were still not smoking after one year is the same for both the antidepressant and placebo groups.

Alternative Hypothesis (H1): The proportion of individuals who were still not smoking after one year is higher for the antidepressant group compared to the placebo group.

Symbolically, in terms of the proportions (p1 for the antidepressant group and p2 for the placebo group):

H0: p1 = p2

H1: p1 > p2

This setup assumes that the antidepressant group has a higher proportion of individuals who successfully quit smoking compared to the placebo group, which is what the study is trying to establish.