Question

If a normal population of overpayments by National Health Insurance Authority to a private health service

provider is known to have a population standard deviation equal to GHC5, how large a sample would we

take in order to be 95% confident that the sample mean overpayment will not differ from the population

mean overpayment by more than ±0.80?

Answer 1

$n=( \frac{Z_{\alpha/2}}{\sigma})^2p(1-p)$

$Z_{\alpha/2}(0.95)=1.65$

$n=(1.65/0.05)^20.8(1-0.8)=174$