Suppose a group of 700 smokers (who all wanted to give up smoking) were randomly

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 115 patients who received the antidepressant drug, 41 were not smoking one year later. Of the 585 patients who received the placebo, 210 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 =0.02 ,

(a) The test statistic is

(b) The P-value is

Explanation / Answer

N = 700 smokers

Here pdrug = 41/115 = 0.3565

pplacebo = 210/585 = 0.3590

p* = (41 + 210)/ 700 = 0.3586

Null Hypothesis : H0 : pdrug - pplacebo = 0

Alternative Hypothesis : Ha : pdrug - pplacebo 0

alpha = 0.02

Test statistic

Z =  (pdrug - pplacebo)/ sqrt [ 0.3586 * 0.6414/700]

= (0.3590 - 0.3565)/ 0.01812 = 0.138

Zcritical = +-2.33

P - value from Z- table => 2 P(pdrug - pplacebo > 0.0025) = 2 * (1 - 0.5555) = 0.889 > 0.02

so we can not reject the null hypothesis and can say that there is noimpact of anti depressant drug.

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