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Topic: [ap-stat] Proofs for APStat Teachers and Others
Replies: 3   Last Post: Jul 23, 2012 11:23 AM

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David Bee

Posts: 4,194
Registered: 12/6/04
re:[ap-stat] Proofs for APStat Teachers and Others
Posted: Jul 23, 2012 11:23 AM
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Among the important results of APStat that teachers should know how
to prove mathematically are the following three:

1. The Central Limit Theorem (CLT)
2. The Chi-Square Test Stat Is Approximately Chi-Square Distributed
3. The T Test Stat Has A Student's t Distribution (exactly so when
sampling from a normal population)

For those still in a proof-reading frame of mind, feel free to
request either of the first two off-List.

Briefly, there are two versions of each: The first for the CLT is
the usual version (sans the rigor of such --- thanks to JS for
making me attentive of such) and is good for those who have not
seen a proof of the CLT before. The second proof of the CLT uses two
applications of L'Hospital's Rule to complete the proof.

Wrt 2 above, the first version is Fisherian in nature (especially
good for those teaching BCCalc) and the second version is Neyman-
Pearsonian in nature and good for those who were introduced to
math-stat from books with such an approach.

Thus, feel free to let me know off-List if you'd like any of the
proofs. (Suggestion: You should request one at a time and request
another one if you were comfortable following the one requested.)

Wrt 3 above, in a way, such might seem like an entire math prob-and-
stat course by itself, and so I'm holding it off for a while. (If
anyone else wants to read and comment on it, then let me know off-
List and I'll forward a copy to you --- btw, it runs six pages,
even though the above theorem [3] and proof of such itself run only
six lines...)

-- David Bee

PS: Please allow for some time for me to respond. (I should be able
to do so within the same day.)

PPS: Thanks to those who have offered comments.

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