As a reply to Dennis' comments:
I wage the same fight in my head each semester about this time, when I'm
introducing hypo. testing to students in my undergrad intro to stats
class. I teach out of Moore and McCabe.
It seems to me that a possible justification for introducing CIs and
hypothesis tests via the z distribution is that we can have the students
calculate p-values, using the standard normal table. Maybe (probably?)
this is self-delusion on my part, but at least the better students might
get a grasp on what a p-value is and what it is not. (No matter how much I
harp on the proper interpretation of CIs and p-values, most of the students
end up exhibiting the obvious misconceptions).
If we deleted the z-test and went right to t-test, I believe that students'
understanding of p-value would be even worse...
Then when you get to t-test, you need to emphasize that this is what people
use, even when the sample is larger than the "magic 30" or whatever magic
number your textbook chose. It is appropriate to use a t-test or CI based
on t distribution in any situation where it was deemed "appropriate" to use
the z-test/CI.
Just my 2 cents...
At 10:58 PM 04/19/2001 -0400, dennis roberts 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 ....
>
>asking something about the population mean when everything we have is an
>estimate ... makes sense ... and is the way to go
>
>in the moore and mccabe book ... the way they go is to use z first ...
>assume population is normal and we know sd ... spend alot of time on that
>... CI and logic of hypothesis testing ... THEN get into applications of t
>in the next chapter ...
>
>i think that the benefit of using z first ... then switching to reality
>... is a misguided order
>
>finally, if one picks up a SRS random journal and looks at some SRS random
>article, the chance of finding a z interval or z test being done is close
>to 0 ... rather, in these situations, t intervals or t tests are almost
>always reported ...
>
>if that is the case ... why do we waste our time on z?
>
>
Christopher J. Mecklin, PhD
Assistant Professor
Department of Mathematics and Statistics
Murray State University
Murray, KY 42071
Phone: 270 762-5437
Fax: 270 762-2314
http://campus.murraystate.edu/academic/faculty/chris.mecklin/index.htm
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