Question

Suppose a group of 700 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 164 patients who received the antidepressant drug, 41 were not smoking one year later. Of the 536 patients who received the placebo, 107 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=0.01

,

(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.

Answer 1

(a) To test the hypothesis as mention in the question, the test statistic is reject H0 if

Where, are the proportion estimates of antipressant drug and placebo respicetively with sample size n1 and n2 respectively and

From the sample, given n1=164, n2 = 536  ,

Therefore,

= 0.038

Therefore, ,

(b) The P_value = 2*P[Z>1.33], since the alternative hypothesis is two tailed, therefore we multiply by 2 since Normal distribution is symmetric. Where Z~N(0, 1)

From the table of standard normal distribution

P_vale = 2*0.0918 = 0.1836

Since the P_value > 0.01 (level of significance), therefore fail to reject H0. Therefore there is no sufficient evidence to determine  whether the antidepressant drug had an effect on changing smoking habits after one year.

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