Thanks so much for all the responses to this posting. Your responses
have been very helpful.
I have computed the Agresti Coull CI's for proportions along with the
naive CI's for proportions and the naive CI's for means (since, in my
case, the proportions in question are really mean proportions, both
approaches seem reasonable).
However, I have obtained CI's with wildly differing widths among these
approaches (holding confidence level, and sample size constant).
Specifically, the Agresti Coull CI's are 3 to 4 times wider than the
naive (unbounded) ones. I'm having a hard time convincing myself that
they both provide 95% coverage.
Any explanations or insight?
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