Calculate expected value for A/B test results
Last updated: October 16, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the p-value.
Twitter/X
October 16, 202537
6
4,974 solved
Given the following scenario about user conversion, calculate the the p-value.
This statistics question from Twitter/X's Technical Screen tests your ability to apply mathematical reasoning to practical problems. The interviewer expects precise definitions, correct methodology, and awareness of assumptions and limitations.
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 explain this result to a non-technical audience?
- What alternative statistical method could you use here?
- What assumptions does this test make, and how would you validate them?
- How would you handle multiple comparisons?
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Problem Formulation
In this scenario, we are asked to calculate the p-value for an A/B test conducted by Twitter/X to evaluate user conversion rates between two groups: Group A (control) and Group B (treatment). We need ...
Solution Approach
To calculate the p-value, we will follow these steps:
- Collect Data: Gather the number of users and conversions for both groups. Let's denote:
- n_A = Number of users in Group A
- x_A = Nu...
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