Definition:Composite Hypothesis

Definition
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.