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:
*H*_{0} : µ_{1}-µ_{2} ≤ 5000
*H*_{1}: µ_{1}-µ_{2} > 5000

where:

µ_{1} = the mean salary of a mathematician in New Jersey

µ_{2} = the mean salary of a mathematician in Virginia

We’ll assume that σ_{1} = $8100 and σ_{2} = $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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