On April 12, 1955, Dr. Jonas Salk released the results of clinical trials for hi

Question

On April 12, 1955, Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent polio. In these clinical trials, 400,000 children were randomly divided into two groups. The subjects in Group 1 were given the vaccine, while the subjects in Group 2 were given a placebo. Of the 200,000 children in the experimental group, 33 developed polio. Of the 200,000 children in the control group, 115 developed polio. Does the evidence support that the vaccine is effective? Use a test statistic and alpha = 0.01.

Explanation / Answer

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 =    0.000165      
p2 = x2/n2 =    0.000575      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    6.08129E-05      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -6.741988826      
          
As significance level =    0.01   , then the critical z is  
          
zcrit =    -2.326347874      
          
Also, the p value is          
          
P =    7.81166*10^-12      
          
As |z| > 2.33, and P < 0.01, we    REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence at 0.01 level that the vaccine is effective. [CONCLUSION]

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