Suppose a group of 700 smokers who all wanted to give up smo

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 399 patients who received the antidepressant drug, 132 were not smoking one year later. Of the 301 patients who received the placebo, 13 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 =0.05, (a) The test statistic is (b) The P-value is

Solution

Formulating the hypotheses          
Ho: p1 - p2   =   0  
Ha: p1 - p2   =/=   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.330827068      
p2 = x2/n2 =    0.043189369      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.026308318      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    10.93333678   [ANSWER, TEST STATISTIC]

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Also, the p value is, as this is two tailed,          
          
P =    7.98569*10^-28 [ANSWER]

[As we can see, this is very close to 0.]