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I have, so far only conducted hypotheses tests having the null hypothesis as a point hypothesis while the research hypothesis is composite.

But what procedure shall I follow if my research hypothesis is a point hypothesis? In particular, my research hypothesis states that the differences in mean of two populations is zero. I wish to test this hypothesis.

Thank you.

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Point hypothesis is always false, since the point is infinitely small, the probability of an effect to be exactly that point is 0.

What you can do is equivalence testing, where you wouldn't test exactly zero, but close to zero within some margin that is close enough for you.

See for example Lakens 2018 https://doi.org/10.1177/2515245918770963 enter image description here but there are many ways to do it. Informally, you can just look if the edges of your confidence interval are close enough to 0

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