How do you describe a critical 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.
Is most powerful test unique?
One test may be the most powerful one for a particular value of an unobservable parameter while a different test is the most powerful one for a different value of the parameter. A uniformly more powerful test remains the most powerful one regardless of the value of the parameters.
How do you find the critical region size?
If the level of significance is α = 0.10, then for a one tailed test the critical region is below z = -1.28 or above z = 1.28. For a two tailed test, use α/2 = 0.05 and the critical region is below z = -1.645 and above z = 1.645.
Which is the best critical region of α?
Let C and D be critical regions of size α, that is, let: Then, C is a best critical region of size α if the power of the test at θ = θ a is the largest among all possible hypothesis tests. More formally, C is the best critical region of size α if, for every other critical region D of size α, we have:
Which is the best critical region for h 0?
Then, if C is a critical region of size α and k is a constant such that: then C is the best, that is, most powerful, critical region for testing the simple null hypothesis H 0: θ = θ 0 against the simple alternative hypothesis H A: θ = θ a. See Hogg and Tanis, pages 400-401 (8th edition pages 513-14).
Which is the critical region of the test?
The test amounts to the following rule: Reject H 0 if an experimental realization x of X falls in the set K ; accept H 0 otherwise (i.e. if x ∈ K ¯ ). The set K is called the critical region of the test; its complement K ¯ is called the acceptance region.
When is a hypothesis rejected in a critical region?
A region of a sample space with the property that if the observed value of a random variable, the distribution of which is connected with the tested hypothesis, falls in that region, then the hypothesis is rejected (cf. Statistical hypotheses, verification of ).