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re:[apstat] Proofs for APStat Teachers and Others
Posted:
Jul 23, 2012 11:23 AM


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 ChiSquare Test Stat Is Approximately ChiSquare 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 proofreading frame of mind, feel free to request either of the first two offList.
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 mathstat from books with such an approach.
Thus, feel free to let me know offList 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 proband 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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