Definition:Acceptance Region

Definition

Let $\theta$ be a population parameter of some population $P$.

Let $\Omega$ be the parameter space of $\theta$.

Let $\mathbf X$ be a random sample from $P$.

Let $T = \map f {\mathbf X}$ be a sample statistic.

Let $\delta$ be a hypothesis test of the form:

accept $H_0$ if $T \in A$

for some null hypothesis $H_0$ and some $A \subset \Omega$.

We refer to $A$ as the acceptance region of $\delta$.