Calculate conditional probability for A/B test results
Last updated: November 30, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the p-value.
Bloomberg
Statistics & Math
Data Scientist
Bloomberg
November 30, 2025Data Scientist
Take-home Project
Statistics & Math
Easy
10
5
4,431 solved
Given the following scenario about user conversion, calculate the the p-value.
Bloomberg values data-driven decision making. This Take-home Project question assesses whether you can design experiments, interpret results correctly, and avoid common statistical pitfalls like p-hacking or Simpson's paradox.
What the Interviewer Expects
- State the correct formula or theorem with clear definitions
- Apply the concept to the given scenario step by step
- Interpret the result in plain language
- Identify assumptions and when they might be violated
Key Topics to Cover
Multiple testing correction (Bonferroni, FDR)
Causal inference basics
Bayesian vs frequentist inference
Power analysis and sample size calculation
Conditional probability and Bayes theorem
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
- What assumptions does this test make, and how would you validate them?
- How would you design a follow-up experiment based on these results?
- What if the sample size is very small?
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Problem Formulation
In this scenario, we are tasked with calculating the p-value for an A/B test evaluating user conversion rates between two groups: A (control) and B (treatment). We denote the conversion rate for group...
Solution Approach
- Collect Data: Assume we have the following data:
- Group A: 200 users, 50 conversions (conversion rate )
- Group B: 200 users, 80 conversions (conversion rate ( p_B = 0.4...
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