Question

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 152 patients who received the antidepressant drug, 36 were not smoking one year later. Of the 748 patients who received the placebo, 189 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.02,

(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

Answer)

P1 = 36/152

P2 = 189/748

N1 = 152, N2 = 748

First we need to check the conditions of normality that is if n1*p1 and n2*p2 both are greater than 5 or not

N1*p1 = 36

N2*p2 = 189

Both the conditions are met, So we can use standard normal z table to estimate the answer

A)

Test statistics z = (p1-p2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = combined proportion = (189+36)/900

After substitution

Test statistics z = -0.41

B)

From z table, P(Z<-0.41) = 0.3409

But our test is two tailed

Ao, P-Value is 2*0.3409 = 0.6818

C)

As the obtained P-Value is greater than the given significance level 0.02

We fail to reject the null hypothesis

So,

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