I have seen tons of situation where the null hypothesis reads along the lines of $\mu = \mu_0$, but what if I wish to test is $\mu \leq \mu_0$? Or more complicated null hypothesis?
For a more concrete example, let's say I have data which I believe is from $N(\mu,1)$, where $\mu$ is unknown. I want to test the null hypothesis that $\mu \leq 0$. How might I do that?