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AP Statistics 4.10.B Interpreting Two-Mean p-Values

Practise interpreting a two-sample p-value as a conditional probability under equal population means, with extremeness matched to the alternative.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • Under equal population means, state the chance of a difference at least as extreme in the claimed direction.

4.10.B—Interpret the p-value of a hypothesis test for the difference between two population means question 1

[Maximum number: 1]

A research scientist is conducting an experiment to determine whether a new chemical process creates less toxic byproduct compared to the current chemical process. The scientist took a random sample of products made with the current chemical process and calculated the sample mean amount of toxic byproduct created. The scientist then took a random sample of products made with the new chemical process and calculated the sample mean amount of toxic byproduct created. The difference in the sample means (current minus new) was 2.31 liters of toxic byproduct. A hypothesis test was conducted using the following hypotheses.

H0:μcurrent −μnew =0Ha:μcurrent −μnew ≠0\begin{aligned} & \mathrm{H}_{0}: \mu_{\text {current }}-\mu_{\text {new }}=0 \\ & \mathrm{H}_{\mathrm{a}}: \mu_{\text {current }}-\mu_{\text {new }} \neq 0 \end{aligned}

Assuming the conditions for inference were met, the scientist calculated the p-value of the test to be 0.072 . Which of the following statements is the best interpretation of the p-value?

A

The probability that the null hypothesis is true is 0.072 .

B

The probability that the alternative hypothesis is true is 0.072.

C

The probability of observing a difference in means of 2.31 liters of toxic byproduct is 0.072.

D

If the null hypothesis is true, the probability of observing a difference in means of at least 2.31 liters of toxic byproduct is 0.072.

E

If the null hypothesis is true, the probability of observing a difference in means of at most 2.31 liters of toxic byproduct is 0.072.

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