Which of the following accurately describes the critical region in hypothesis testing?

• A. The set of all values of the test statistic that leads to rejection of the $H$₀ (null hypothesis)
• B. The interval estimate for a population parameter
• C. The range of values where the $H$₀ (null hypothesis) is accepted
• D. The set of all possible values of the population mean $\mu$

Answer: (A)

Verified step by step guidance

1. Understand that in hypothesis testing, the critical region (also called the rejection region) is the set of values for the test statistic that would lead us to reject the null hypothesis \(H_0\).
2. Recall that the null hypothesis \(H_0\) represents a statement of no effect or no difference, and the alternative hypothesis \(H_a\) represents what we want to test for.
3. The critical region is determined based on the significance level \(\alpha\), which defines the probability of rejecting \(H_0\) when it is actually true (Type I error).
4. Values of the test statistic that fall into this critical region are considered extreme enough to provide sufficient evidence against \(H_0\), leading to its rejection.
5. Therefore, the critical region is not an interval estimate, nor is it the range where \(H_0\) is accepted, nor the set of all possible population means; it specifically refers to the set of test statistic values that cause rejection of \(H_0\).