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Notation for one-sided hypothesis testing

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I see the following notation for one-sided hypothesis testing:

  • $H_0$: $K = 2$
  • $H_1$: $K > 2$

I would find it more natural to write:

  • $H_0$: $K \le 2$
  • $H_1$: $K > 2$

Assume a situation where $K$ is not, by definition, limited to equal or be higher than two. $K$ is just a dummy variable and 2 a dummy number.

Where does the first notation come from and why is it in use?

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