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.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): composite hypothesis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): composite hypothesis
• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $9.1$: Problems of Testing Hypotheses: Definition $9.1.2$