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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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Testing a Difference Other Than Zero

In the previous example, we were just testing whether or not there was any difference between the two populations. We can also test whether the difference exceeds a certain value. As an example, suppose we want to test the hypothesis that the average salary of a mathematician in New Jersey exceeds the average salary in Virginia by more than $5,000. We would state the hypotheses as follows:
H0 : µ12 ≤ 5000
H1: µ12 > 5000
where:
µ1 = the mean salary of a mathematician in New Jersey
µ2 = the mean salary of a mathematician in Virginia
We’ll assume that σ1 = $8100 and σ2 = $7600, and we’ll test this hypothesis at the α = 0.10 level.
 
A sample of 42 mathematicians from New Jersey had a ...

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