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Topic: [ap-stat] 30 and the Central Limit Theorem
Replies: 6   Last Post: Mar 23, 2012 7:21 PM

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Jared Derksen

Posts: 1,648
Registered: 2/5/06
Re:[ap-stat] 30 and the Central Limit Theorem
Posted: Mar 22, 2012 1:25 PM
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Chris:

This is helpful. And interesting! As usual, your reference knowledge is
impressive.

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?

Cheers!

JD

On Thu, Mar 22, 2012 at 10:05 AM, Chris Olsen <COlsen@mchsi.com> wrote:

> Jared and All ?****
>
> ** **
>
> The ?30 is enough? goes all the way back to a very early publication by
> Student (Wm Gossett). In an article somewhere in the vicinity of 1922 or
> so, he says something like, ??and with sample sizes are about 30, one can
> use the normal curve.?****
>
> ** **
>
> Another Wm, Wm Cochrane, has an article that pretty much justifies the
> number 30.****
>
> ** **
>
> Sorry, I don?t have either reference at hand, and I?m kinda pressed for
> time. But if anyone would like the refs, send me an e-mail and I?ll try
> to hit the library or search my office back at Grinnell. We?re on break,
> so don?t hold your breath?****
>
> ** **
>
> **n **Chris ****
>
> ** **
>
> *From:* Jared Derksen [mailto:mrmathman@gmail.com]
> *Sent:* Thursday, March 22, 2012 9:57 AM
> *To:* AP Statistics
> *Cc:* AP Statistics
> *Subject:* Re: [ap-stat] Question regarding normality check for a two
> sample t-test****
>
> ** **
>
> 30 comes from 30 lines of text on a t-table. Books with smaller font used
> 40...****
>
> ** **
>




--
Jared Derksen

I understand the need for conformity. Without a concise set of rules to
follow we would probably all have to resort to common sense. --David
Thorne

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