Question

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. if the p is high, the null will fly.
d. the p - value separates the critical region from the values that do not lead to rejection of the null hypothesis

Explanation:

• Option A: The P - value is indeed an area under the sampling distribution curve. For example, in a z - test or t - test, it is the area corresponding to the test statistic.
• Option B: The common rule in hypothesis testing is that if the P - value ($P$) is less than the significance level ($\alpha$) (i.e., "if the $P$ is low"), we reject the null hypothesis. So, "if the $P$ is low, the null must go" is a valid mnemonic.
• Option C: If the P - value ($P$) is greater than the significance level ($\alpha$) (i.e., "if the $P$ is high"), we fail to reject the null hypothesis. So, "if the $P$ is high, the null will fly" is a valid mnemonic.
• Option D: The significance level ($\alpha$) (not the P - value) separates the critical region (rejection region) from the non - critical region (values that do not lead to rejection of the null hypothesis). The P - value is compared with the significance level to make a decision about the null hypothesis.

Answer:

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