I have many (250) instances of an experiment in which a binary random variable is the output. I selected a sampling of 80 instances and verified the result in every case to be success. I suspect that all 255 instances are success, but I cannot be sure without testing all of them.
Question: Based on testing only these 80 instances, how can I calculate a confidence level that all 250 instances are success? Is this even possible?
I tried using the confidence interval formula for a Bernoulli random variable, but because all instances sampled were success, I came up with the confidence interval (1,1) for any alpha level, which isn't what I'm looking for.
More generally, how do you deal with the situation where all samples are of the same class? The problem isn't that my sample size is too small--it's just that a seemingly large majority of instances (potentially 100%) are successes.
