Dear all,
I have a problem that I haven't seen in the literature and would like some guidance if possible.
We have a known population, relatively small with, say 200 individuals. We sample a large proportion (110) of these and look for the characteristic of interest. No individuals are found to possess this characteristic (r=0, n=100, N=200)
What I need to know is what is the CI on the estimated proportion of zero.
The method given in Armitage and Berry (p121) gives 95 % limits between 0 and 2.7%. However, as we are sampling a large section of the population intuition would tell us that we should be more confident in the point estimate and that the confidence interval should be narrower (the finite population correction).
Finite population corrections that I have tracked down seem to be limited to textbook normal distributions and approximations to it. Obviously, here we are at one extreme of a binomial distribution.
Any suggestions would be greatly appreciated.
Best wishes
Guy
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Guy J Forrester, Biometrician,
Landcare Research
Gerald St.
Lincoln PO Box 69
Canterbury
New Zealand
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