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Consider 3 different samples. Each sample is independent.

1: 23, 25, 21, 22, 21, 22, 20, 23, 19, 22, 19, 21

2: 28, 27, 27, 29, 26, 29, 27, 30, 28, 27, 26, 29

3: 23, 20, 25, 21, 22, 23, 21, 20, 19, 20, 22, 21

I am being asked to test whether μ2 - μ1 = μ3 - μ2 with 99% confidence. How am I meant to perform this test? I know how to test for the difference of means, that's quite simple, but how does one test for the difference of differences?

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# Hypothesis test for the difference of the difference of means?

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