dennis roberts wrote:
>
> the fundamental issue here is ... is it reasonably to expect ... that when
> you are making some inference about a population mean ... that you will
> KNOW the variance in the population?
No, Dennis, of course it isn't - at least in the social sciences and
usually elsewhere as well. That's why I don't recommend
teaching this (recall my comments about "dangerous scaffolding") to
the average life-sciences student who needs to know how to use the test
and what it _means_, but not the theory behind it.
In the case of the student with some mathematical background, who may
actually need to do something theoretical with the distribution one day
(and may actually have the ability to do so) I would introduce t by way
of Z.
A rough guide; If this group of students know what a maximum-likelihood
estimator is, and have been or will be expected to derive, from first
principles, a hypothesis test or confidence interval for (say) a
singleton sample from an exponential distribution, then they ought to be
introduced by way of Z.
If not, then:
(a) don't do it at all, or
(b) put your chalk down and talk your way through it as an Interesting
Historical Anecdote without giving them anything to write down.
Draw a few pictures if you must.
Or
(c) give them a handout with "DO NOT USE THIS TECHNIQUE!" written on it
in big letters.
(I've tried all four approaches, as well as the wrong one.)
-Robert Dawson
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