One Tailed, Two Tailed t-Tests

Date: 09/11/98 at 22:12:44
From: Cindy Newman
Subject: t test - one tail vs. two tail 

What is the difference between a one-tailed and two-tailed t test? Our 
teacher has shown us how to do the t-test but can't explain why the two 
tests are different or when to use which one. Can you help? 

Date: 09/12/98 at 07:54:17
From: Doctor Anthony
Subject: Re: t test - one tail vs. two tail 

The tables for a t-test always give two-tailed values, so a 5% test is 
actually 2.5% in each tail. If you want a 5% one-tailed test you 
should look up the t value corresponding to a 10% test.

How do you decide whether to do a one-tailed or two-tailed test? The 
answer is to look at the alternative hypothesis. I will use the 
convention that H0 represents the null-hypothesis and H1 represents 
the alternative hypothesis.

Suppose the question is worded as follows: Test if the single sample 
value 15.4 is taken from a normal population with mean 15.0 and known 
variance 0.09.

Here H0 is that it comes from a population of mean 15.0 and H1 is that 
it comes from a population of mean different from 15.0. There is no 
mention that it comes from a population of mean higher or lower 
than 15.0 - just different from 15.0  and so we do a two-tailed test.

Suppose instead that the question states: Test if a sample taken from 
a production line of light bulbs after a new process has been 
introduced shows an improvement in the life of the product.

Here we are concerned with an increase in life so:

   H0 is that life of bulbs is unchanged.
   H1 is that mean life is greater than before.  

We do a one-tailed test.

So we need to look at the alternative hypothesis to decide if a 
one-tailed or two-tailed test is required.

- Doctor Anthony, The Math Forum
Check out our web site! http://mathforum.org/dr.math/