Question

Suppose a group of 800 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 220 patients who received the antidepressant drug, 17 were not smoking one year later. Of the 580 patients who received the placebo, 271 were not smoking one year later. Given the null hypothesis ?0:(?????−????????)=0H0:(pdrug−pplacebo)=0 and the alternative hypothesis ??:(?????−????????)≠0Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use ?=0.04α=0.04.

(a) The test statistic is

(b) The P-value is

(c) The final conclusion is

A. There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group.
B. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.

Answer 1

The sample proportions for the 2 groups here are computed as:
p₁ = 17/220 = 0.0773
p₂ = 271/580 = 04672

The pooled proportion is computed as:
P = (17 + 271) / (220 + 580) = 0.36

The standard error here is computed as:

a) The test statistic here is computed as:

Therefore -10.26 is the required test statistic value here.

b) The p-value for this 2 tailed test, here is computed from the standard normal tables as:

p = 2P(Z < -10.26) = approx. 0

Therefore 0 is the required p-value here.

c) As the p-value here is < 0.04 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here.

d) As the test is significant, There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group.