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 rules") 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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