What is the definition of rejection region?
John Hall
Updated on February 09, 2026
A rejection region is an area of a graph where you would reject the null hypothesis (assuming your test results fall into that area).
What is acceptance and rejection region?
The subset that is considered to be consistent with the null hypothesis is called the “acceptance region”; another subset is called the “rejection region” (or “critical region”). If the sample outcome falls into the acceptance region, then the null hypothesis is accepted.
What is critical region or rejection region?
A critical region, also known as the rejection region, is a set of values for the test statistic for which the null hypothesis is rejected. i.e. if the observed test statistic is in the critical region then we reject the null hypothesis and accept the alternative hypothesis.
What is the region of non rejection?
(2) Definition: The nonrejection region is the set, or range, of values of the test statistic for which the null hypothesis H0 is not rejected, or retained.
What is meant by acceptance region?
The acceptance region is the interval within the sampling distribution of the test statistic that is consistent with the null hypothesis H 0 from hypothesis testing. It is the complementary region to the rejection region.
What is the rejection region and why is it important?
The rejection region is the region where, if our test statistic falls, then we have enough evidence to reject the null hypothesis. If we consider the right-tailed test, for example, the rejection region is any value greater than c 1 − α , where c 1 − α is the critical value.
How do I get acceptance region?
How to Find the Region of Acceptance
- Estimate population variance.
- Compute standard error.
- Choose a significance level.
- Find the critical value.
- Find the upper limit (UL) of the region of acceptance.
- In a similar way, we find the lower limit (LL) of the range of acceptance.
What is acceptance region example?
The range of values that leads the researcher to accept the null hypothesis is called the region of acceptance. For example, a researcher might hypothesize that the population mean is equal to 10. To test this null hypothesis, he/she could collect a random sample of observations and compute the sample mean.
How is the rejection region of a statistic defined?
When large values of a test statistic W ( X) represent evidence against the null hypothesis, the rejection region can be equivalently defined as R = x ∈ X; W ( x) ≥ c ( α) for some constant c ( α) depending on the chosen significance level α and the distribution of W ( X) under the null hypothesis.
What is a rejection region in a null hypothesis?
What is a Rejection Region? A rejection region (a.k.a. critical region) in a Null Hypothesis Statistical Test is a part of the parameter space such that observing a result that falls under it will lead to the rejection of a the null hypothesis.
Which is an alias for a rejection region?
Aliases: critical region. A rejection region (a.k.a. critical region) in a Null Hypothesis Statistical Test is a part of the parameter space such that observing a result that falls under it will lead to the rejection of a the null hypothesis.
What is the power function of a rejection region?
The power function of a hypothesis test with a rejection region R is a function of θ defined by β (θ) = Pθ (X ∈ R). A good test should have a power function close to 0 for all θ ∈ Θ 0 and 1 for all θ ∈ Θc0 so that both type I and type II errors are low.
