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How do you find the critical region?
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.
What is the critical region or regions of the sampling distribution?
The critical region of the sampling distribution of a statistic is also known as the α region. It is the area, or areas, of the sampling distribution of a statistic that will lead to the rejection of the hypothesis tested when that hypothesis is true.
What is the critical region 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 difference between critical value and critical region?
A critical value is a point on the distribution of the test statistic under the null hypothesis that defines a set of values that call for rejecting the null hypothesis. This set is called critical or rejection region. Usually, one-sided tests have one critical value and two-sided test have two critical values.
How do you determine the rejection region?
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.
What is the critical value at the 0.05 level of significance?
The level of significance which is selected in Step 1 (e.g., α =0.05) dictates the critical value. For example, in an upper tailed Z test, if α =0.05 then the critical value is Z=1.645.
What is a critical value on a graph?
A critical value is a line on a graph that splits the graph into sections. One or two of the sections is the “rejection region“; if your test value falls into that region, then you reject the null hypothesis.
How is critical value determined?
The critical value is computed based on the given significance level α and the type of probability distribution of the idealized model. The critical value divides the area under the probability distribution curve in rejection region(s) and in non-rejection region.
How do you know if Z score is significant?
a z-score less than or equal to the critical value of -1.645. Thus, it is significant at the 0.05 level. z = -3.25 falls in the Rejection Region. A sample mean with a z-score greater than or equal to the critical value of 1.645 is significant at the 0.05 level.
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 p.d.f of an exponential random variable?
The p.d.f. of an exponential random variable is: for x ≥ 0. Under the hypothesis H: θ = 3, the p.d.f. of an exponential random variable is: for x ≥ 0. Because we can uniquely specify the p.d.f. under the hypothesis H: θ = 3, the hypothesis is a simple hypothesis.