Calculate conditional probability for A/B test results
Last updated: February 28, 2026
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
Brex
February 28, 202645
5
258 solved
Given the following scenario about user conversion, calculate the the sample size needed.
Statistics questions at Brex test your ability to reason quantitatively and design rigorous experiments. This Onsite question evaluates your understanding of statistical inference and its application to business decisions.
What the Interviewer Expects
- Derive results from first principles when needed
- Handle complex scenarios with multiple interacting variables
- Design experiments that account for real-world complications
- Discuss advanced topics: Bayesian methods, causal inference, resampling
- Connect statistical concepts to business decision-making
- Identify subtle errors in reasoning (Simpson's paradox, survivorship bias)
Key Topics to Cover
How to Approach This
- Define your hypotheses (H0 and H1) clearly before performing any test.
- Calculate required sample size BEFORE running an experiment, using power analysis.
- Remember the Central Limit Theorem: sample means become approximately normal with large n.
- Watch for Simpson's paradox. Always segment data by key dimensions.
- Distinguish between statistical significance and practical significance.
Possible Follow-up Questions
- How would you handle multiple comparisons?
- What if the sample size is very small?
- How would you explain this result to a non-technical audience?
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Problem Formulation
In this scenario, we need to determine the sample size required for an A/B test to evaluate user conversion rates. Let denote the conversion rate for group A (control) and for grou...
Solution Approach
To calculate the required sample size, we will use the formula for sample size in a two-proportion z-test:
[ N = \left( \frac{(Z_{\alpha/2} + Z_{\beta})^2 \cdot (p_1(1 - p_1) + p_2(1 - p_2))}{(p_2 -...
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