Question

HW 31 #1

Suppose a group of 900 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 379 patients who received the antidepressant drug, 85 were not smoking one year later. Of the 521 patients who received the placebo, 151 were not smoking one year later. Given the null hypothesis H0:(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 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

Ans:

sample proportion(drug)=85/379=0.2243

sample proportion(placebo)=151/521=0.2898

pooled proportion=(85+151)/(379+521)=0.2622

a)Test statistic:

z=(0.2243-0.2898)/SQRT(0.2622*(1-0.2622)*((1/379)+(1/521)))

z=-2.21

b)p-value=2*P(z<-2.21)=0.0274

c)As,p-value<0.05,we reject the null hypothesis.

Option A is correct.

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.