There is at least two very good pedagogical reasons for teaching z
tests. Both the z and t tests are based on normality - the t test is
used only because the model standard deviation is unknown or rather,
there is no assumed value for it. Whether or not this is in practice
'always' the case is irrelevant from the point of view of understanding
what is going on. 'In an ideal world' we would do z tests! But in
practice we usually cannot assume a value for sigma, so we are forced to
use a t test. This is less powerful than the z test. So we pay a price
for the lack of knowledge - if we don't know sigma, we pay for this in
lowered power of the test.
As a general principle, this is a fundamental aspect of statistics - I
rate it as one of the reasons why students learn statistics! Lack of
knowledge costs!
So the two good reasons are - that the z test is the basis for the t,
and the understanding that knowledge has a very direct value.
I hasten to add that 'knowledge' here is always understood to be
'assumed knowledge' - as it always is in statistics.
My eight cents worth.....
Alan
--
Alan McLean ([EMAIL PROTECTED])
Department of Econometrics and Business Statistics
Monash University, Caulfield Campus, Melbourne
Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
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