In this section, you will consider the following options for null hypothesis and corresponding alternate hypothesis with respect to the unknown value \(\mu\text{:}\)
\begin{equation*}
H_0 : \mu = \mu_0 \\ H_a: \mu \neq \mu_0
\end{equation*}
or
\begin{equation*}
H_0 : \mu \le \mu_0 \\ H_a: \mu \gt \mu_0
\end{equation*}
or
\begin{equation*}
H_0 : \mu \ge \mu_0 \\ H_a:\mu \lt \mu_0
\end{equation*}
Again, we choose only one of these three options and as before the first is called a "two-tailed" test and the last two are called "one-tailed" tests. Note that some people will write all of these null hypothesis options using equality but the alternate hypothesis determines the number of tails.