Question

A medical researcher wants to do a study on the proportion of knee replacement surgeries that causes complications. How many surgeries should he sample to estimate the proportion to within 4% with 95% confidence?

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.04

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.96/0.04)^2
n = 600.25

sample size = 600 (if rounding is done to nearest integer)