Hello
I have an epidemiology question which is outside my normal realm of statistics. The problem appears fairly simple, and hopefully for any epidemiologist or probability expert out there it is, although the answer is not obvious to me. I apologise if I am missing the obvious.....
I have n animals which have all been tested for a disease and all have come back negative.
The sensitivity of the test is 0.7 (probability of a true postive)
The specificity is 1.0 (probability of a true negative)
The probability of a false negative is therefore 1 - 0.7 = 0.3
The probability of a false positive is 1 - 1 = 0
What we'd like to know is the probability that all animals tested are truly negative?
Bayes theorem requires the knowledge of the prevalence of the disease which we don't know. I suspect the hypergeometric distribution is going to play a part but having performed an online search haven't been able to find anything which answers this question.
I would appreciate any suggestions on how to approach this problem.
Thank you very much
Carole
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