Re: Propotion CI when sample p(p-1) = 0

How do I handle a proportion CI when my sample p=1?
It is an accuracy test. The equipment is very
y accurate. Time constraints are a driver in test
design. At lower sample sizes often the accuracy
will be 100%. I don't infer that the population will
be 100%, but how is CI calculated when p(1-p)=0?


You obviously mean the case where X = 0 or X = N. The assumption is that X ~ Bin(p,N) with unknown parameter p.

If X = N, the 1-alpha confidence interval for p is

(alpha)^(1/N) < = p <= 1.

If X = 0, the 1-alpha confidence interval for p is

0 <= p <= 1 - (alpha)^(1/N).

Jack
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