What does a p-value of 0.03 mean at alpha 0.05?

WHAT THIS TESTS: This question checks whether you can interpret a frequentist p-value literally and act on it correctly. Many senior engineers and data scientists conflate p-values with Bayesian posterior probabilities, so the interviewer wants to hear a disciplined, mechanical definition tied to the null hypothesis.

A GOOD ANSWER COVERS four things in order. First, the exact definition: a p-value of 0.03 means that if the null hypothesis is true (meaning the new feature has absolutely no effect on the metric), there is a 3 percent probability of observing a test result at least as extreme as the one you actually saw. Second, the comparison to alpha: you pre-registered a significance level of 0.05, which is your threshold for how much false-positive risk you are willing to tolerate. Third, the decision rule: because 0.03 is less than 0.05, you reject the null hypothesis and conclude the result is statistically significant. Fourth, the practical caveat: statistical significance does not guarantee business significance, so you should still look at effect size and confidence intervals before shipping the feature.

COMMON WRONG ANSWERS: The most dangerous red flag is interpreting 0.03 as the probability that the null hypothesis is true. Under frequentist inference, the null is either true or false; the p-value does not assign a probability to it. Another red flag is saying there is a 97 percent chance the feature works or that you are 97 percent confident in the result; that language describes Bayesian credible intervals, not p-values. A subtler error is forgetting the pre-registered alpha entirely and treating 0.03 as magically good without referencing your 0.05 decision boundary.

LIKELY FOLLOW-UPS: The interviewer may ask what you would do if the p-value were 0.06, which tests whether you understand that 0.05 is a convention, not a physical law, and whether you would discuss statistical power and sample size. They may also ask how you would explain this result to a non-technical executive without using jargon, or how you would guard against multiple-comparison problems if you ran twenty variants instead of one.

ONE CONCRETE EXAMPLE: Imagine you are testing a new checkout button color. The null hypothesis is that the conversion rate is identical for both colors. You run the experiment and observe a 2 percentage point lift with a p-value of 0.03. You say: if the button color truly makes no difference, we would see a lift this big or bigger only 3 percent of the time by random noise alone. Because our pre-defined alpha is 5 percent, and 3 is below that threshold, we reject the null and treat the lift as statistically significant. We would still check whether a 2 point lift justifies the engineering cost of a permanent change.