Infer distribution and choose robust statistics
Company: Google
Role: Data Scientist
Category: Statistics & Math
Difficulty: Medium
Interview Round: Technical Screen
A dataset of n=10,000 session revenues (USD) has: 65% zeros; mean=8.5; median=0; p90=30; p95=120; p99=620. (a) Propose a plausible generative model (e.g., zero-inflated log-normal with a Pareto tail) and justify it from the summaries. (b) Outline two quick validation checks (e.g., QQ-plot after log1p, Hill estimator for tail index) and what patterns you expect. (c) Choose a transformation for modeling incremental lift and defend it. (d) Construct an approximate 95% CI for the median using order-statistic/binomial bounds; provide the indices and numeric bounds you’d report. (e) For an A/B test with equal n and an observed +3% lift in the mean but no change in the median, pick an appropriate hypothesis test and explain why a Welch t-test might mislead; quantify when a permutation or Wilcoxon test is preferable. (f) Under your chosen model, estimate P(revenue > 50) and discuss sensitivity to tail assumptions.
Quick Answer: This question evaluates a candidate's ability to infer underlying distributions from summary statistics and apply robust statistical reasoning including handling zero-inflation, tail behavior, transformation choices, confidence-interval construction, hypothesis test selection, and sensitivity analysis for skewed revenue data.