This is probably one of the more straight forward questions on here but here it is: I want to use a random number generator to sample X number of charts to look for the # occurrences of Y event. So let's say I randomly sample 100 charts, and 18% of them contain Y (or alternatively Y occurs X# of times within a sample of 100). How do I determine how confident I can be that this is the true estimate of the population of events (I may or may not have an exact population N.
Additionally, or equally important, how can I estimate the apriori number of cases which need to be randomly sampled to have a sufficient confidence interval ?
I know G power can be used for this but I just need some clarification on the process.
Many thanks
Hint: the CI for a proportion within a binomial distribution can be estimated using the normal approximation
$$\hat p \pm z\sqrt{\frac{\hat p(1-\hat p)}{n}}$$
where $\hat p$ is the proportion of events of interest estimated from the sample, $z$ is the $1-\frac{1}{2}\alpha$ percentile of a standard normal distribution (1.96 for the 95% CI), $\alpha$ is the predefined error percentile, and $n$ represents the sample size.