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Is the significance level the rejection region?
Our significance level corresponds to the area under the tail that is exactly equal to α: if we use our normal criterion of α = . 05, then 5% of the area under the curve becomes what we call the rejection region (also called the critical region) of the distribution.
What determines the rejection region?
For a hypothesis test, a researcher collects sample data. 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.
How does significance level affect hypothesis testing?
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.
How to test the rejection region of a hypothesis?
The rejection region method 1 Express the claim about a specific value for the population parameter of interest as a null hypothesis, denoted NH. 2 Express the alternative claim as an alternative hypothesis, denoted AH. 3 Calculate a test statistic based on the assumption that the null hypothesis is true.
Can a hypothesis be rejected at the significance level?
Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.
When to reject or reject the null hypothesis?
Let’s return finally to the question of whether we reject or fail to reject the null hypothesis. If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis.
Which is the default value for hypothesis testing?
For the sake of argument, we use 5% as a default value for hypothesis tests in this course (unless stated otherwise). The significance level dictates the critical value (s) for the test, beyond which an observed t-statistic leads to rejection of the null hypothesis in favor of the alternative.