I am uncertain about the solution to the problem for which I am trying to
solve. I am hoping that someone might help guide me to the correct
solution.
I have a discrete distribution (say 100) with a dichotomous population
(either good or bad). There is no knowledge of the population split until
after sampling. Since the testing of each sample cost time and money, only
one sample set will be taken. I want to find the smallest sample size that
has a 90% probability of being indicative of the entire population.
The distribution seems like it would be a hypergeometric distribution (since
I do not know the sample size, I do not know if a binomial distribution
would be appropriate in this case). The information I have read on
confidence intervals does no seem to be directly applicable to
hypergeometric distributions. The method of maximum likelihood seems like a
method to relate the sample population to the entire population, but it does
not provide for determining the most efficient sample size and it does not
indicate the accuracy of the sample distribution as compared to the entire
population distribution.
If you can help me solve this problem, I would greatly appreciate it.
Thank you for your time.
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