Solution
What a p-value Means
Show the problem again
A hypothesis test yields p = 0.03. Which is the correct interpretation: (a) there is a 3% chance the null hypothesis is true, (b) there is a 3% chance the result is due to chance, or (c) something else? Answer a, b, or c.
Worked solution
The answer is (c). A p-value is the probability of observing data at least this extreme, assuming the null hypothesis is true: P(data ≥ this extreme | H₀), not P(H₀ | data). Interpretation (a) inverts the conditioning, converting one to the other requires a prior via Bayes' theorem, and (b) is a vaguer version of the same error. Small p means the data would be surprising under the null; it says nothing directly about how probable the null is.
Source: Standard interpretation question; the framing follows the American Statistical Association's statement on p-values (2016). Statement written for AxiomIQ.