Why does a large p-value not mean the null hypothesis is true?

Because the test is designed to evaluate whether the evidence is strong enough to go against the null, not to prove the null is correct.

A high p-value means the observed sample would not be unusual if the null hypothesis were true. That is much weaker than saying the null has been verified.

There are several reasons a test might produce a large p-value:

• the null is actually true
• the sample is too small
• the data are noisy
• the true effect exists but is modest

Suppose fictional insurer Cedar Point Assurance tests whether average claims fraud has increased. If the p-value is 0.24, the correct statement is that the analyst fails to reject the null at common significance levels. The correct statement is not that fraud definitely has not increased.

That wording discipline matters on CFA questions because the exam often tests interpretation more than arithmetic.