In this section, you will consider the following options for null hypothesis and corresponding alternate hypothesis with respect to the unknown value p:
\begin{equation*}
H_0 : p = p_0 \\ H_a : p \neq p_0
\end{equation*}
or
\begin{equation*}
H_0 : p \le p_0 \\ H_a : p \gt p_0
\end{equation*}
or
\begin{equation*}
H_0 : p \ge p_0 \\ H_a : p \lt p_0.
\end{equation*}
For any given problem, we choose only one of these three options. The first is called a "two-tailed" test since the alternate hypothesis can not be equal if it is actually larger or smaller. The last two are called "one-tailed" tests since the alternate hypothesis only allows for being on one side. Note that some people will write all of these null hypothesis options using equality but the alternate hypothesis determines the number of tails.