One Tailed, Two Tailed t-TestsDate: 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/ |
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