Date: Fri, 27 Apr 2007 16:48:43 -0400
Reply-To: Peter Flom <firstname.lastname@example.org>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Peter Flom <peterflomconsulting@MINDSPRING.COM>
Subject: Central Limit Theorem
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I am reviewing and editing a statistics book.
In it, they have the following statement re the central limit theorem
"Regardless of the shape of the population, if a sufficiently large random sample of size n is taken from the population, then the sample is approximately normally distributed, with mean mu sub xbar and standard deviation sigma/sqrt(n)"
This seems completely wrong!
The CLM is not about ONE sample, but about MANY samples. That is, it should be
"Regardless of the shape of the population, if a sufficiently large NUMBER of samples of a particular size is taken, then the distribution of the mean of the SAMPLES approaches normal as the NUMBER of samples approaches infinity"
I googled a bit, and did not find a really good clear statement of this - the book is intended for HS students.
Anyone got any suggestions? Am I all wrong? Is the author all wrong? Are we BOTH wrong?