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Bill Morris  wrote:

> Loosely speaking, isn't the standard error of the mean at a given level an 
indicator of the  probability that the _mean_ lies within a specified range? 
We would expect the distribution of the means to be smaller than the 
distribution of the samples.
>
> I took n to be 30, rather than 30-1, as 30 seemed to qualify as a "large 
sample." The 1.96 gives us exactly 95%, versus your 2 SD and 95.45% (in case 
anyone is confused about where the figures come from).
>
> You seem to be writing about the probability that a given _observation_ lies within a specified range. 
>   

Hmmm, I should read more carefully next time (must have been my 
eye-sight), I was triggered by the 95% and thought you were talking 
about Standard Deviation, but you did mention Standard Error indeed. 
Sorry about that and for causing any confusion here....

As far as I remember the calculation - (1.96 x SD/root n) - should be 
done using the Sample Standard Deviation (which is the one where SD is 
calculated using the "n minus one" division), but that is just 
nitpicking in this case (the range will become slightly larger by a 
factor of app. 1.068, but despite that the outcomes will still not overlap).

Nicol�s


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