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What kind of null hypothesis can be tested using a Student's t?

It's very likely to be one of the questions of the statistics exam. In order to test a null hypothesis using the Student's t, does it need to have particular features?

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1 Answer 1

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What kind of null hypothesis can be tested using a Student's t?

Generally speaking we're testing means in some way -

For example, a one-sample test of a population mean being equal to a specified value, or a two sample test of equality of population means (both under normal assumptions). However, t-tests arise in other contexts, such as ANOVA and regression.

In order to test a null hypothesis using the Student's t, does it need to have particular features?

Two situations could have an identical null hypothesis but require different tests. The null hypothesis itself is not the only determinant of which test is suitable.

For example, consider a test of equality of means for two gamma-distributed variables, or two Bernoulli-distributed variables. In both cases, you can phrase the null as a equality of population means, but you normally wouldn't do a t-test for either.

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