Suppose a group of 800 smokers (who all wanted to give up smoking) were randomly

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 392 patients who received the antidepressant drug, 15 were not smoking one year later. Of the 408 patients who received the placebo, 171 were not smoking one year later. Given the null hypothesis H0:(pdrugpplacebo)=0 and the alternative hypothesis Ha:(pdrugpplacebo)0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use =0.01,

(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.

Explanation / Answer

P1 = 15/392 = 0.038

P2 = 171/408 = 0.419

pooled sample proportion P = (p1 * n1 + p2 * n2 )/(n1 + n2)

= (0.038 * 392 + 0.419 * 408)/(392 + 408)

= 0.23

SE = sqrt (P * (1 - P) * (1/n1 + 1/n2))

= Sqrt (0.23 * 0.77 * (1/392 + 1/408))

= 0.03

A) The test statistic Z = (p1 - p2)/SE

= (0.038 - 0.419)/0.03

= -12.7

B) p-value = 2 * P(Z < -12.7)

= 2 * 0 = 0

C) As the p-value is less than the alpha value 0.01, SO the null hypothesis is rejected.

Option-B is correct.

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