Question

question 18 which of the following describes the critical region? a outcomes with very low probability if the null hypothesis is true b outcomes with a high probability if the null hypothesis is true c outcomes with very low probability whether or not the null hypothesis is true d outcomes with a high probability whether or not the null hypothesis is true

Explanation:

In hypothesis testing, the critical region is defined as the set of outcomes that are unlikely to occur if the null hypothesis is true. If an outcome falls within this region, we reject the null hypothesis.

• Option A: This is correct. The critical region consists of outcomes with very low probability when the null hypothesis ($H_0$) is true.
• Option B: Incorrect. High - probability outcomes when $H_0$ is true would not lead us to reject $H_0$, so they are not in the critical region.
• Option C: Incorrect. The definition of the critical region is based on the assumption that the null hypothesis is true. It's not about the probability regardless of $H_0$.
• Option D: Incorrect. High - probability outcomes (whether $H_0$ is true or not) are not in the critical region.

Answer:

A. outcomes with very low probability if the null hypothesis is true