Questions: Which of the following is NOT true about P-values in hypothesis testing? Choose the correct answer below. A. The P-value is an area. B. If the P is low, the null must go. C. The P-value separates the critical region from the values that do not lead to rejection of the null hypothesis. D. If the P is high, the null will fly.

Which of the following is NOT true about P-values in hypothesis testing?

Choose the correct answer below.
A. The P-value is an area.
B. If the P is low, the null must go.
C. The P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.
D. If the P is high, the null will fly.

Transcript text: Which of the following is NOT true about P-values in hypothesis testing? Choose the correct answer below. A. The $P$-value is an area. B. If the $P$ is low, the null must go. C. The P-value separates the critical region from the values that do not lead to rejection of the null hypothesis. D. If the $P$ is high, the null will fly.

Solution

Solution Steps

To determine which statement is NOT true about P-values in hypothesis testing, we need to evaluate each option based on the definition and properties of P-values.

A. The P-value is an area.

This is true because the P-value represents the probability of obtaining test results at least as extreme as the observed results, under the assumption that the null hypothesis is correct. This probability is represented as an area under the probability distribution curve.

B. If the P is low, the null must go.

This is a common mnemonic indicating that if the P-value is low (typically less than the significance level, e.g., 0.05), we reject the null hypothesis. This is true.

C. The P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.

This is NOT true. The P-value itself does not separate the critical region; rather, it is compared to the significance level to determine whether the test statistic falls in the critical region.

D. If the P is high, the null will fly.

This is another mnemonic indicating that if the P-value is high, we fail to reject the null hypothesis. This is true.

Therefore, the correct answer is C.

Step 1: Evaluate Each Statement

We need to analyze the truth of each statement regarding P-values in hypothesis testing:

Statement A: The $ P $-value is an area.
- This statement is true because the $ P $-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. This probability corresponds to an area under the probability distribution curve.
Statement B: If the $ P $ is low, the null must go.
- This statement is also true. A low $ P $-value (typically $ P < \alpha $, where $ \alpha $ is the significance level) indicates strong evidence against the null hypothesis, leading us to reject it.
Statement C: The $ P $-value separates the critical region from the values that do not lead to rejection of the null hypothesis.
- This statement is NOT true. The $ P $-value itself does not define the critical region; rather, it is used to determine whether the test statistic falls within the critical region based on a predetermined significance level.
Statement D: If the $ P $ is high, the null will fly.
- This statement is true. A high $ P $-value suggests that there is not enough evidence to reject the null hypothesis, leading us to fail to reject it.