How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Onsite rounds at Meta.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

Compare Bayesian and frequentist decisions

Quick Overview

This question evaluates understanding of Bayesian inference versus frequentist hypothesis testing, decision theory under asymmetric loss, sequential monitoring/optional stopping, and prior elicitation applied to A/B testing within the Statistics & Math domain.

A/B Test With Beta–Binomial Posteriors and Decision-Making Under Asymmetric Costs

You ran a two-arm A/B test on a binary KPI with independent Beta(1, 1) priors for each arm. Each arm saw 10,000 users. You observed 515 conversions in arm A and 500 in arm B.

Assume "lift > 0" means that the treatment arm A has a higher true conversion rate than control arm B: Δ = p_A − p_B.

Answer the following:

(a) Compute the posterior distribution for each arm and the posterior probability that lift > 0.

(b) Define a decision rule that minimizes expected loss when the costs of a false positive (shipping a worse variant) and a false negative (failing to ship a better variant) are asymmetric.

(c) Contrast the resulting Bayesian decision with a frequentist two-proportion test, especially under optional stopping. Discuss operational implications (e.g., communicating posterior vs. p‑value, sequential monitoring/alpha spending).

(d) How would you set or elicit priors to avoid over‑optimism in future experiments?

Quick Overview

A/B Test With Beta–Binomial Posteriors and Decision-Making Under Asymmetric Costs

You ran a two-arm A/B test on a binary KPI with independent Beta(1, 1) priors for each arm. Each arm saw 10,000 users. You observed 515 conversions in arm A and 500 in arm B.

Assume "lift > 0" means that the treatment arm A has a higher true conversion rate than control arm B: Δ = p_A − p_B.

Answer the following:

(a) Compute the posterior distribution for each arm and the posterior probability that lift > 0.

(b) Define a decision rule that minimizes expected loss when the costs of a false positive (shipping a worse variant) and a false negative (failing to ship a better variant) are asymmetric.

(d) How would you set or elicit priors to avoid over‑optimism in future experiments?

Compare Bayesian and frequentist decisions

Quick Overview

A/B Test With Beta–Binomial Posteriors and Decision-Making Under Asymmetric Costs

Solution

Submit Your Answer to Earn 20XP

Compare Bayesian and frequentist decisions

Quick Overview

A/B Test With Beta–Binomial Posteriors and Decision-Making Under Asymmetric Costs

Solution

Submit Your Answer to Earn 20XP