In article <[EMAIL PROTECTED]>,
dennis roberts <[EMAIL PROTECTED]> wrote:
>students have enough problems with all the stuff in stat as it is ... but,
>when we start some discussion about sampling error of means ... for use in
>building a confidence interval and/or testing some hypothesis ... the first
>thing observant students will ask when you say to them ...
>
>assume SRS of n=50 and THAT WE KNOW THAT THE POPULATION SD = 4 ... is: if
>we are trying to do some inferencing about the population mean ... how come
>we know the population sd but NOT the mean too? most find this notion
>highly illogical ... but we and books trudge on ...
>
>and they are correct of course in the NON logic of this scenario
>
>thus, it makes a ton more sense to me to introduce at this point a t
>distribution ... this is NOT hard to do ... then get right on with the
>reality case ....
I don't find this persuasive. I think that any student who has the
abstract reasoning ability needed to understand the concepts involved
will not have any difficult accepting a statement that "this situation
doesn't come up often in practice, but we'll start with it because
it's simpler".
I have my doubts that introducing the t distribution is "NOT hard", if
by that you mean that it's not hard to get them to understand what's
actually happening. Of course, it's not very hard to get them to
understand how to plug the numbers into the formula.
I think one could argue that introducing the z test first is MORE
realistic. The situation where there are "nuisance" parameters that
affect the distribution of the test statistic but are in practice
unknown is TYPICAL. It's just a lucky break that the t statistic
doesn't depend on sigma. After seeing the z test, students will
realize how lucky one is to have such a statistic, and will realize
that one shouldn't expect that to happen all the time. (Well, the
really good ones might realize all this.)
Radford Neal
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