Calculate conditional probability for A/B test results
Last updated: January 8, 2026
Quick Overview
Given the following scenario about user conversion, calculate the the p-value.
HRT
January 8, 202644
11
721 solved
Given the following scenario about user conversion, calculate the the p-value.
HRT 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
- Set up the problem formally with proper notation
- Apply the correct statistical test with clear justification
- Interpret results with appropriate caveats and confidence levels
- Discuss practical significance vs statistical significance
- Identify potential confounders and how to address them
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
- What alternative statistical method could you use here?
- How would you handle multiple comparisons?
- What assumptions does this test make, and how would you validate them?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To analyze the conversion rates from an A/B test, we will consider two groups of users: Group A (control group) and Group B (treatment group). Let:
- : Number of users in group A
- ...
Solution Approach
To calculate the p-value, we can use a two-proportion z-test, which is appropriate for comparing the proportions of two independent groups. The steps are as follows:
- Compute the conversion rates f...
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