Question

If it is desired to estimate a risk difference to an environmental exposure in two industrial groups, how large a sample should be selected in each group for the estimate to be within 5 percentage points of the true difference with 95% confidence, when no reasonable estimates of exposure risks for either group are available?

Answer 1

p̂ 1 =       0.5  
p̂ 2 =       0.5  
margin of error ,   E=   0.05  
confidence level,   C =   0.95  
          
alpha=   1-C=   0.05  
Z value at α/2=   Z(α/2) =    1.960   [excel formula =normsinv(α/2)]
          
Sample Size,n1=n2 = n = [ p̂1 * (1 - p̂1) + p̂2 * (1-p̂2)]*(Z/E)²     =   768.29  
          
So,Sample Size needed=       769  

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thanks