Yet, p=0 is a special case where an outcome is impossible. A reasonable
confidence interval for p should not include zero if the outcome has been
observed in a sample. Not so?
-Dale
----- Original Message -----
From: Donald Burrill <[EMAIL PROTECTED]>
To: Dale Berger <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Wednesday, June 21, 2000 12:27 AM
Subject: Re: Rates and proportions
> On Tue, 20 Jun 2000, Dale Berger wrote:
>
> > If we observe one escape out of 1250 inmates, why can't we reliably
> > rule out zero as the population escape rate?
>
> Because k = 1 (for n = 1250) is not significantly different from k = 0.
>
> > The normal approximation to the binomial may not be appropriate here.
>
> No, I don't expect it is. So use the binomial distribution.
>
> That's supposing that one wants a statistical argument. If a purely
> logical argument suffices, it is indeed the case that a counterexample
> demonstrates the falsity of a proposition. But it may still be not
> unreasonable to ask, with what probability may one observe one (or more)
> escapes outof n=1250 (or whatever n actually applies), if the true
> probability of an escape is <some suitably small non-zero value>?
> (I specify non-zero only because it's difficult to carry out some
> computations when p=0 exactly.)
> And it is certainly reasonable to ask what confidence interval on p is
> associated with k = 1.
> -- Don.
> ------------------------------------------------------------------------
> Donald F. Burrill [EMAIL PROTECTED]
> 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
> MSC #29, Plymouth, NH 03264 603-535-2597
> 184 Nashua Road, Bedford, NH 03110 603-471-7128
>
>
>
>
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