For a sample of 100 patients that have undergone a particularsurgical procedure,

Question

For a sample of 100 patients that have undergone a particularsurgical procedure, 18 suffered serious side effects due tothe operation.

(a) Compute a 95% confidence interval for the true proportion ofpatients that will suffer serious side effects due to this type ofsurgery.

(b) In the estimation of the true proportion of patients thatwill suffer serious side effects due to this type of surgery,we want to be 95% confident that the error does not exceed2.5%. What is the required sample size.

Explanation / Answer

Given n=100, p=18/100=0.18 =0.05, |Z(0.025)|=1.96 (check normal table) ------------------------------------------------------------------------------ (a) The 95% CI is p ± Z*p*(1-p)/n --> 0.18 ± 1.96*sqrt(0.18*(1-0.18)/100) --> (0.105, 0.255) ------------------------------------------------------------------------------ (b) Given E=0.025 n=(Z/E)^2*p*(1-p) =(1.96/0.025)^2*0.18*(1-0.18) =907.2323 Take n=908

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