Suppose that variable $X$ is normally distributed. With sample data done from $X$, we want to do null hypothesis testing $H_0: \mu = \mu_0$, where $\mu_0$ is some constant, and $H_1: \mu < \mu_0$. True standard deviation is known as $\sigma = \sigma_0$.
When $H_1 : \mu \neq \mu_0$, I could see how hypothesis testing would go, but this time $\mu>\mu_0$ is not being considered, and I do not know how this test should be. One of my texts seems to suggest that the hypothesis testing case should be equivalent to testing $H_0: \mu \geq \mu_0$. Is this true?
