Question

Explain why the procedure for a one-sample t-test involves comparing the mean of the sample you have to a world in which the null hypothesis is true. (Why don’t we compare the mean of the sample you have to a world in which the research hypothesis is true?)

Answer 1

We know that,

There are two kinds of hypotheses for a one sample t-test, the null hypothesis and the alternative hypothesis. The alternative hypothesis assumes that some difference exists between the true mean (μ) and the comparison value (m0), whereas the null hypothesis assumes that no difference exists.

Also,

The purpose of the one sample t-test is to determine if the null hypothesis should be rejected, given the sample data.

Hence, Procedure for a one-sample t-test involves comparing the mean of the sample you have to a world in which the null hypothesis is true.