Question

a) [6 marks] Suppose a group of 900 smokers (who all wanted to quit smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 148 patients who received the antidepressant drug, 23 were not smoking one year later. Of the 752 patients who received placebo, 97 were not smoking one year later. Conduct a test of hypotheses (state H, and Ha) to see if taking an antidepressant drug can help smokers to quit smoking. (a = 5%) Here is the data summary Population х Х P 1 (drug) 148 23 2 (placebo) 752 97 Total 900 n n b) [2 marks] State your conclusion:

Answer 1

Answer:

Given,

sample proportion p1^ = x1/n1 = 23/148 = 0.16

p2^ = x2/n2 = 97/752 = 0.13

p = (x1+x2)/(n1+n2) = (23+97)/(148+752) = 0.133

Ho : p1 - p2 = 0

Ha : p1 - p2 != 0

test statistic z = (p1^ - p2^)/sqrt(p(1-p)(1/n1 + 1/n2))

substitute values

= (0.16 - 0.13)/sqrt(0.133(1-0.133)(1/148 + 1/752))

= 0.98

P value = 0.3270861 [since from z table]

= 0.3271

Here p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.