I colleague has come to me with a question which I have answered for him but the only statistics I have done was what I did at school and a one semester course on Bayesian methods at university, so I wanted to post the question here and see if my answer is correct.
- I have a population of $10,000$ animals.
- I want to test for a disease for which I have a test which is $100$% effective.
- If the disease is present in the population then prevalence of the disease will be $20$%.
How many tests must I perform to be sure to $3\sigma$, and $5\sigma$ significance that the disease is not present?
I suggested applying Bayes theorem, I have typed up my attempted solution here