A biologists are planning a study to estimate the proportion of an animal species that are infected a bacterial pathogen. He has come up with a way to obtain blood samples from a simple random sample of animals in the target population. He agrees in wanting an estimate of the percent infected that is accurate to within plus or minus four percentage points (or less), nineteen times out of twenty.
What sample size should he recommend for this study?
sqrt((0.5)(0.5)/n) = 0.04
n = 156
Why is this approach not correct?