Question: What is the most powerful critical region?

A test defined by a critical region C of size is a uniformly most powerful (UMP) test if it is a most powerful test against each simple alternative in the alternative hypothesis . The critical region C is called a uniformly most powerful critical region of size .

What is the critical region of?

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 the critical region Alpha?

➢ 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. If the level of significance is α = .

What is a critical value in stats?

A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval, or which defines the threshold of statistical significance in a statistical test.

What does p value 0.05 mean?

P > 0.05 is the probability that the null hypothesis is true. A statistically significant test result (P ≤ 0.05) means that the test hypothesis is false or should be rejected. A P value greater than 0.05 means that no effect was observed.

What is a 5% significance level?

The significance level, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

What is the critical value for a 95% confidence interval?

1.96 The critical value for a 95% confidence interval is 1.96, where (1-0.95)/2 = 0.025.

What is the 10 significance level?

Common significance levels are 0.10 (1 chance in 10), 0.05 (1 chance in 20), and 0.01 (1 chance in 100). The result of a hypothesis test, as has been seen, is that the null hypothesis is either rejected or not. The significance level for the test is set in advance by the researcher in choosing a critical test value.

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