What is the region of rejection determined by?

What is the region of rejection determined by?

Statistics Dictionary From the sample data, the researcher computes a test statistic. If the statistic falls within a specified range of values, the researcher rejects the null hypothesis . The range of values that leads the researcher to reject the null hypothesis is called the region of rejection.

What is the importance of the rejection and the acceptance region in stating a decision in a test of hypothesis?

Results from a statistical tests will fall into one of two regions: the rejection region— which will lead you to reject the null hypothesis, or the acceptance region, where you provisionally accept the null hypothesis.

What is the region of rejection and how do we use it?

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 difference between 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 are rejection regions?

The rejection region is the interval, measured in the sampling distribution of the statistic under study, that leads to rejection of the null hypothesis H 0 in a hypothesis test.

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.

Which is on the right side of the reject region?

In this situation, the rejection region is on the right side. So, if the test statistic is bigger than the cut-off z-score, we would reject the null, otherwise, we wouldn’t. To sum up, the significance level and the reject region are quite crucial in the process of hypothesis testing.

What is the rejection region for the null hypothesis?

in the test of the null hypothesis that the mean is the particular value μ 0. The rejection region for a two-sided alternative is t = ˉx – μ0 (s / √n) (t ≤ t n – 1, α / 2) or (t ≥ t n – 1, 1 – α / 2).

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.