-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On
Behalf Of Alan Miller
Sent: Tuesday, April 30, 2002 4:32 PM
To: [EMAIL PROTECTED]
Subject: Re: Is Hogg and Craig Wrong?
David Heiser wrote in message ...
>Been doing a little cross checking between sources on the confidence
>interval about sample means, where the sample (n) comes from a normal
>population with unknown mean and unknown variance.
>
>Several textbooks give the confidence interval about the sample mean as
>t*s/sqrt(n), where n is the number in the sample, t is the t distribution
>value at n-1 df, and s is the sample unbiased standard deviation.
Using either n or (n-1) in the denominator gives a BIASED estimate of the
standard deviation.
Using sumsq/(n-1) gives an unbiased estimate of the variance.
Using sqrt( sumsq/(n-1.5) ) gives an estimate of the standard deviation
which is almost unbiased.
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Interesting idea. Did you mean 0.5 or 1.5? I can see the 0.5, but not the
1.5. Has this been looked at for small samples via Monte Carlo approaches to
determine if it gives a better approximation to the hypothetical population
normal distribution sigma value?
DAHeiser
.
.
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