What is critical or rejection region?
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 do you call the point where the critical region starts?
The z-scores that designate the start of the critical region are called the critical values . If the sample mean taken from the population falls within these critical regions, or “rejection regions,” we would conclude that there was too much of a difference and we would reject the null hypothesis.
What does rejection region mean?
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 does the rejection region depend on?
What Does the Rejection Region Depend on? The area that is cut-off actually depends on the significance level. Say the level of significance, α, is 0.05. Then we have α divided by 2, or 0.025 on the left side and 0.025 on the right side.
What is the critical value of 0.01 level of significance?
Hypothesis Test For a Population Proportion Using the Method of Rejection Regions
| a = 0.01 | a = 0.05 | |
|---|---|---|
| Z-Critical Value for a Left Tailed Test | -2.33 | -1.645 |
| Z-Critical Value for a Right Tailed Test | 2.33 | 1.645 |
| Z-Critical Value for a Two Tailed Test | 2.58 | 1.96 |
What’s the difference between rejection and critical value?
The threshold value that helps in this decision is called the critical value. This value divides the region under the normal curve into two parts: rejection region and acceptance region. The region under the normal curve is called the rejection region if the test statistic results in the rejection of the null hypothesis.
Is the rejection region on the right side of the curve?
The shaded region or the critical region is equal to the significance level (α). The next figure again shows the rejection region for the one-tailed test and how the critical value appears on it: Here the curve shows that it is a right-tailed test, so the rejection region appears on the right side of the curve.
Where is the rejection region on a one tailed test?
If the test is two-tailed, the rejection area lies under both the tails. A further level of significance decides the size of the critical region. The greater the level of significance, the larger the area of rejection will be. The figure below shows the rejection region for the one-tailed test and how the critical value appears on it:
Which is the maximal probability of the critical region?
The probability of the critical region is α. In the case of a composite null hypothesis, the maximal probability of the critical region is α. Compute from the observations the observed value tobs of the test statistic T. Decide to either reject the null hypothesis in favor of the alternative or not reject it.