I've been reading around about hypothesis testing. I don't understand why the following one sided tests are equivalent:
$H_0:\mu \leq \mu_0$; $H_a:\mu > \mu_0$
$H_0:\mu = \mu_0$; $H_a:\mu > \mu_0$
Edit: I think I understand why they are equivalent. Anything that's rejected by the second hypothesis will be also rejected by the first (at least for Z tests and T tests you learn about in a first course in stats). Maybe a better question to ask is -- are there scenarios where these two inferences are not equivalent?