Match the following:
1: With a small P-value,
2: With a large P-value,

Question

BlackTom AI · Accepted Answer

In this matching item, we pair each statement label with the corresponding interpretation of the P-value.
1: With a small P-value. A small P-value indicates that the observed data are unlikely under the null hypothesis, which leads to rejecting H0. Therefore, the statement that fits here is: 'We reject H0. There is evidence that the true property of the population is different from what was stated in H0.'
2: With a large P-value. A large P-value suggests that the observed data do not provide strong evidence against the null hypothesis, so we fail to reject H0. The matching statement for this is: 'We cannot reject H0.'
To validate the logic, consider that the P-value measures the probability, under the assumption that H0 is true, of obtaining data as extreme or more extreme than what was observed. Small P-values (typically below a chosen significance level) favor concluding that H0 is unlikely and thus are used to justify rejection. In contrast, large P-values indicate that the data are compatible with H0, and there is insufficient evidence to reject it. The two provided answer phrases align with these standard interpretations, yielding the correct pairings as described above.

ECON 3640-090 Spring 2025 Lecture #18 Warm-Up

Match the following: 1: With a small P-value, 2: With a large P-value,

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