Explain p‑values to a product manager

Walk a product manager through what a two-sided A/B test p-value of 0.03 actually means and, just as important, what it does not mean. Use this concrete example: baseline conversion 5.0%, observed lift +0.4 percentage points, pooled standard error 0.18 percentage points, two-sided p=0.03. Cover: (a) the null hypothesis, the test statistic, the sampling distribution, and the 'extremeness under the null' interpretation. (b) why $p \ne \Pr(H_0 \mid \text{data})$ and why p is not the false positive rate for this single result. (c) the relationship between p-values, confidence intervals, alpha, and statistical power (and why a small p does not imply a large effect). (d) how optional stopping/peeking and multiple looks inflate type I error and how to communicate that risk. (e) provide the plain-language 2–3 sentence explanation you would actually say to the PM, and a contrasting Bayesian framing for the same result.

This question assesses a candidate's command of hypothesis testing and p-value interpretation, statistical inference ideas (such as null hypothesis framing, test statistics, sampling distributions, and how p-values, confidence intervals, alpha, and power connect), awareness of experiment-design pitfalls like optional stopping and multiple looks, and the skill of explaining these points to a non-technical product manager in a Data Scientist role within the Statistics & Math domain. Interviewers ask it frequently because they need evidence that a candidate can avoid and correct common misreadings—for example, confusing a p-value with the probability of the null hypothesis given the data, or treating a small p as proof of a large effect—and the required level is mainly conceptual understanding with applied communication and interpretation, not implementation-level computation.