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RE: [apstat] 30 and the Central Limit Theorem
Posted:
Mar 22, 2012 2:57 PM


Jared 
Jared asks, 30 and CLT.

So does a more nuanced explanation go like this?
There are some mathematical and historical reasons to believe that when n > 30, this is a safe point at which to believe that a sample mean is becoming approximately normal.
However, we still like to graph our data, when possible, as an indication of how skewed the population might be. And how confident we are that the mean we are working with has an approximately normal distribution.
And the practice switching from t to z at 30 (or 40) is an artifact of a lack of inadequate technology. Now that we can easily compute t for any sample size, there is no need act as if something magically changes at 30.
Is that more complete?
Gosh, that sounds great to me! (I think the historical reason would be that Student thought it reasonable.)
n Chris
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