Some of the discussion from this list got copied to EdStat-L and people have been responding there. Here is one response I thought was worth repeating.
----- Forwarded message from David S. Moore -----
>>The text book we are using says use the z- distribution when ever the >sample size exceeds 30 and the distribution is normal. Let sample s >approximate population sigma. How come the t- table in the AP booklet >has degrees of freedom entries way past 30 ??? what am I missing??
The AP stat tables come directly from The Basic Practice of Statistics. I didn't stop at df = 30 for the obvious reason given by Paul Velleman: whenever you estimate sigma from the data, for any n, you are using t not z.
As n increases, t approaches z, but rounding all the way to df=infty for any n > 30 may not be reasonable. A selection of intermediate df's allows rounding up to the next largest df and also assessing what the effect of rounding to df=infty would be. Many texts (like BPS) have 1-page t-tables that allow this, as Don Burrill remarks. If your text bases t vs z on n rather than on s versus sigma, and doesn't discuss the robustness of t to non-normality that makes t procedures often reasonable in practice, you should look at more modern texts. (And I think we should all be using software or capable calculators that make tables anachronistic in any event.)
----- End of forwarded message from David S. Moore -----
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