described a study of staph infections in surgery patients Th

described a study of staph infections in surgery patients. The researchers recruited 917 patients who had tested positive for Staphylococcus aureus and randomly assigned them to receive a nasal ointment that contained either a staph-killing solution or a placebo. Postsurgery infections with S. aureus were then recorded. In the treatment group, 17 of 504 patients developed a staph infection, compared with 32 of 413 patients in the placebo group

Calculate a 95% confidence interval for the difference between the proportions of postsurgical staph infections among patients receiving a staph-killing ointment or a placebo.

Solution

ANS) .. for the treatment group, proportion = p1 = 0.03373016....
   for the plaebo group, proportion = p2 = 0.07748184....

standard error = sqrt [ (p1*(1-p1) / 504 ) + ( p2*(1-p2) / 413 ) ] = 0.01541878...

z-score for 95% conf. interval = 1.96..

confidence interval = [ ( p2-p1) - (1.96*0.01541878) , ( p2-p1) + (1.96*0.01541878) ]

= [ 0.01353087 ,  0.07397249 ]......