Chris Olsen wrote:
> It would seem to me that more than this most can be said. If my reading
> of the central limit theorem is up to snuff, I should be able to use the
"Z
> test with s" without an underlying assumption of the normality of the
parent
> population,
Yes, as an unnecessary approximation,
> required for the t.
and no. The utility of either test for non-normal populations depends on
the central limit theorem and related results. "Z with s" relies on the same
assumptions about the sampling distribution of s and mu that the t test
does.
> I am not etching n = 30 in stone, here
Good... There are distributions (ie, the normal distributions) for which
n=1 suffices. There are distributions (eg. lottery prizes) for which n=10000
is too small. If t won't work for a population, z-with-s won't either.
> but there is _some_ large n that will make the underlying sampling
> distribution of the mean sufficiently close to normal to justify the "Z
with
> s."
No - at least not if you mean "there is some large n independent of the
distribution..."
-RJMD
