\begin{definition}[Definition:Composite Hypothesis]
Let $\theta$ be a population parameter of some population. 
Let the parameter space of $\theta$ be $\Omega$. 
Let $\Omega_0$ and $\Omega_1$ be disjoint subsets of $\Omega$ such that $\Omega_0 \cup \Omega_1 = \Omega$. 
Consider the hypotheses: 
:$H_0: \theta \in \Omega_0$
:$H_1: \theta \in \Omega_1$
We call $H_i$, for $i \in \set {0, 1}$, a '''composite hypothesis''' if $\Omega_i$ contains more than a single element.
\end{definition}