Which of the following statements provides the correct definition of a $p$-value?

A researcher tests whether a new cognitive-behavioral intervention reduces test anxiety. After analyzing the data, she obtains a p-value of 0.04 and states: 'There is only a 4% probability that the intervention has no real effect.' This is a correct interpretation of the p-value.

A researcher conducts a study on the effect of sleep on memory and finds a $p$-value of .03. Match each of the following statements about this result to its correct logical status.

A researcher studying the effects of a new study technique on memory scores finds a result of $p = .03$. To avoid the 'inverse probability' fallacy, the researcher must carefully analyze the logic of the result. Arrange the following steps in the correct logical order to reach a valid interpretation of this $p$-value.

An expert evaluating a psychological study that reports a $p$-value of .03 flags the author's claim that 'there is a 3 percent probability that the null hypothesis is true' as a logical error. The expert correctly notes that the $p$-value actually describes the probability of the ______ assuming that the null hypothesis is true.

The $p$-value represents the probability that the null hypothesis is true.

A student researcher finds a result with $p = .03$ and concludes, 'This means there is only a $3\%$ chance that the null hypothesis is true.' What is the conceptual error in this student's interpretation?

A researcher studying cognitive performance under stress reports a result of $p = .04$. Match the following descriptions to their correct scientific status.

A student researcher reviews a psychology paper and finds the statement: 'Since $p = .02$, there is a $2\%$ probability that the null hypothesis is true.' In analyzing this error, the student notes that instead of measuring the probability of the observed sample result if the null hypothesis were true, the author has incorrectly interpreted the $p$-value as the probability of the _____.

A peer reviewer evaluates a manuscript where the author concludes that a treatment is effective because 'the probability of the null hypothesis being true is only $p = .03$.' Order the steps the reviewer should take to evaluate and correct this interpretation.

Describe the frequent misinterpretation of the $p$-value and state its actual definition.

Diagnose the conceptual error in the student's conclusion and explain what the $p$-value of .04 actually means in this context.

If a researcher obtains a sample result and wants to report the $p$-value correctly, how should they phrase the definition of this $p$-value without claiming it measures the truth of the null hypothesis?