Question

Suppose a group of 1000 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 358 patients who received the antidepressant drug, 174 were not smoking one year later. Of the 642 patients who received the placebo, 64 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.05.

(a) The test statistic is

(b) The P-value is

(c) The final conclusion is

A. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.
B. 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.

Answer 1

Here we can use ti-83 calculator.

P1 = drug

P2 = Placebo

Test Hypothesis :

H0: p1 = p2

Ha : p1 ≠p2

a) Test statistic :

Z = 13.75

b) p-value :

P= 0.0000 = 0

c) conclusion :

P-value is less than alpha=0.05 then reject the null hypothesis (H0).

Therefore,

B. 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.