What does critical region mean in statistics?
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 null hypothesis in a likelihood ratio test?
The likelihood ratio test is a test of the sufficiency of a smaller model versus a more complex model. The null hypothesis of the test states that the smaller model provides as good a fit for the data as the larger model.
How did you determine the critical region?
➢ To determine the critical region for a normal distribution, we use the table for the standard normal distribution. 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 then t = -1.725 and t = 1.725.
Which is the critical region for the likelihood ratio test?
Then, the likelihood ratio is the quotient: And, to test the null hypothesis H 0: θ ∈ ω against the alternative hypothesis H A: θ ∈ ω ′, the critical region for the likelihood ratio test is the set of sample points for which: where \\ (0 < k < 1\\), and k is selected so that the test has a desired significance level α.
When to use L in a likelihood ratio test?
L ( Ω ^) denote the maximum of the likelihood function with respect to θ when θ is in the entire parameter space Ω. Then, the likelihood ratio is the quotient: And, to test the null hypothesis H 0: θ ∈ ω against the alternative hypothesis H A: θ ∈ ω ′, the critical region for the likelihood ratio test is the set of sample points for which:
How to test the likelihood ratio of honey?
Previous experience suggests that the volume X, the volume in fluid ounces of a randomly selected jar of the company’s honey is normally distributed with a known variance of 2. Derive the likelihood ratio test for testing, at a significance level of α = 0.05, the null hypothesis H 0: μ = 10 against the alternative hypothesis H_A: \\mu ≠ 10\\).
When to reject the null hypothesis in likelihood ratio test?
Now, the likelihood ratio test tells us to reject the null hypothesis when the likelihood ratio λ is small, that is, when: where k is chosen to ensure that, in this case, α = 0.05. Well, by taking the natural log of both sides of the inequality, we can show that λ ≤ k is equivalent to: