450000 Vasectommies are performed each year A following stud

450,000 Vasectommies are performed each year. A following study had the following results: of 21,300 men who have had not a vasectomy, 69 were found to have prostate cancer and of 22,000 men who have had a vasectomy, 133 were found to have prostate cancer.

a. Construct a 99% confidence interval for the difference in the proportion of men that got cancer in the group that had vasectommies and the proportion of men that got cancer in the group that did not have vasectommies

Solution

For the   99%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.005      
z(alpha/2) =    2.575829304

Also, the standard error of the difference is          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.00065171      
      
          
lower bound = (p1-p2) - z(alpha/2) * sd = -0.004484711      
upper bound = (p1-p2) + z(alpha/2) * sd   -0.001127325      
          
Thus, the confidence interval is          
          
(-0.004484711,-0.001127325) [ANSWER]