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 271 patients who received the antidepressant drug, 65 were not smoking one year later. Of the 729 patients who received the placebo, 89 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

a)

p1cap = X1/N1 = 65/271 = 0.2399
p1cap = X2/N2 = 89/729 = 0.1221
pcap = (X1 + X2)/(N1 + N2) = (65+89)/(271+729) = 0.154

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.2399-0.1221)/sqrt(0.154*(1-0.154)*(1/271 + 1/729))
z = 4.59

b)

P-value Approach
P-value = 0
As P-value < 0.02, reject the null hypothesis.

c)

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.