In a clinical trial of a vaccine 10000 children were randoml

In a clinical trial of a vaccine, 10,000 children were randomly divided into two groups. The subjects in group 1 (the experimental group) were given the vaccine while the subjects in group 2 (the control group) were given a placebo. Of the 5,000 children in the experimental group, 84 developed the disease. of the 5,000 children in the control group, 117 developed the disease.

Determine the test statistice

z0 = ?

round to two decimal places as required

Solution

Here, we see that pdo =    0   , the
hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.0168      
p2 = x2/n2 =    0.0234      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.002806072      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -2.352042296 = -2.35 [ANSWER]