----- Forwarded message from Olsen, Chris -----
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, required for the t. I am not etching n = 30 in stone, here --
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."
----- End of forwarded message from Olsen, Chris -----
(x-bar minus hyp.x-bar)/sigma approaches a normal distribution but
(x-bar minus hyp.x-bar)/s approaches t if x is normal. If x is not
normal, it is true that (x-bar minus hyp.x-bar)/s eventually
approaches a normal distribution, too, but so does t. This leaves it
an open question whether the mystery distribution is betwen the t
approaching z or t'other side of t from z yet still approaching z.
1/x, 2/x and 3/x all aproach 0 for large n. The fact that 3/x
approaches 1/x does not mean it ever gets closer than 2/x does.
_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College MSC#29
| | Plymouth, New Hampshire 03264 USA
| * | Rural Route 1, Box 10
/ | Ashland, NH 03217-9702
| ) (603) 968-9914 (home)
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