Explain p-values and interpret regressions

Question

This is a rapid-fire statistics onsite for a Data Scientist role. Address every part clearly and precisely: first give the explanation you would offer a Product Manager, then the version for a technical audience.

Part A — p-values

1. Describe what a p-value is in everyday language that a PM can follow.
2. State the formal definition of a p-value.
3. How should a p-value be interpreted, and which common misinterpretations should you avoid?
4. Suppose you run an A/B test and the primary metric gives $p = 0.03$. What would you decide? What extra context would you ask for before shipping?

Part B — Linear regression with confounding 5. You fit a linear regression with several features and you suspect confounders are present. How do you interpret each coefficient? 6. What is actually meant by "controlling for other variables," and under what circumstances can that interpretation break down? 7. What distinguishes an associational interpretation of a coefficient from a causal one? 8. Which checks or methods would you use to reduce confounding bias?

Part C — L1 vs L2 regularization 9. What are L1 (Lasso) and L2 (Ridge) regularization, and how do their effects differ? 10. When and why would you choose one over the other, considering feature selection, multicollinearity, and prediction versus interpretability? 11. How would you choose the regularization strength ($\lambda$), and what practical tradeoffs are involved?

Overview: A PayPal Data Scientist onsite statistics rapid-fire covers p-values, including a plain-language and formal definition, common misinterpretations, and an A/B-test decision at $p = 0.03$; interpreting linear-regression coefficients in the presence of confounding, including associational versus causal readings, failure modes of "controlling for" other variables, and approaches to reduce bias; and L1 versus L2 regularization, plus how to select the penalty strength. It probes both statistical depth and the ability to communicate with product and technical audiences.