The boundaries of the critical region are determined by

The boundaries of the critical region are determined by

• A. The alpha level
• B. The sample size
• C. The observed effect size
• D. The number of groups

Answer: (A)

The boundaries of the critical region come from the significance level you choose, the alpha level. This sets how extreme a result must be under the null hypothesis to be considered evidence against it. In practice, alpha determines the cutoff values (the critical values) on the test statistic’s null distribution. If the observed test statistic falls beyond those cutoffs, you reject the null. For example, with a typical two-sided test at alpha = 0.05, the critical region is the outer 2.5% on each tail, so the boundaries are the 2.5th and 97.5th percentiles of the null distribution. The observed effect size is just where your data land relative to those boundaries; it doesn’t set the boundaries themselves. The sample size and the number of groups can affect the shape of the null distribution (and thus the exact critical values in some tests), but the alpha level still defines the boundary you’re using to decide rejection.

The boundaries of the critical region come from the significance level you choose, the alpha level. This sets how extreme a result must be under the null hypothesis to be considered evidence against it. In practice, alpha determines the cutoff values (the critical values) on the test statistic’s null distribution. If the observed test statistic falls beyond those cutoffs, you reject the null.

For example, with a typical two-sided test at alpha = 0.05, the critical region is the outer 2.5% on each tail, so the boundaries are the 2.5th and 97.5th percentiles of the null distribution. The observed effect size is just where your data land relative to those boundaries; it doesn’t set the boundaries themselves. The sample size and the number of groups can affect the shape of the null distribution (and thus the exact critical values in some tests), but the alpha level still defines the boundary you’re using to decide rejection.