Q&A #3831


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From: Pat Ballew (for Teacher2Teacher Service)
Date: May 01, 2000 at 18:01:17
Subject: Re: Statistics

I assume you are using the N=30 as a point of demarcation to decide when to
use a t-interval (n<30) and when to use a z-interval.  The N=30 is a rule of
thumb and only tells you that for values above n=30 the Z and T critical
values will be "approximately" the same... (compare it to rules like np>5 and
n(1-p)>5 for binomial approximations... they are all just "approximation

  MY OPINION (not shared by ALL teachers of statistics).. with modern
technology (even hand held calculators can be used to compute t-intervals) it
is NEVER appropriate to use z-intervals in place of t-intervals..

 The purpose of a t-test (small sample test?) is to compensate for the fact
that we do not know the true population standard deviation, and must
approximate it with the standard deviation of the population, S.  As N gets
larger the t-distribution does get very close to the normal curve, and at some
value it makes so little difference that either will give almost the same
results, so it is not a question of accuracy, but of understanding why we use
the t, and when we can use z.

I hope this is clear.  I'm sure it would be more easily understood if you
could see the "arm waving" that goes with it but technology has not reached
that level yet..
Good Luck.

 -Pat Ballew, for the Teacher2Teacher service

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