Calculate conditional probability for user retention
Last updated: November 6, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the p-value.
Postmates
November 6, 2025152
4
4,723 solved
Given the following scenario about revenue per session, calculate the the p-value.
This statistics question from Postmates's Phone 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
- 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
- How would you handle multiple comparisons?
- How would you design a follow-up experiment based on these results?
- 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
To calculate the conditional probability for user retention based on revenue per session, we need to define our variables clearly. Let:
- = Revenue per session
- = User retention (1 if...
Solution Approach
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Data Collection: Gather data on user sessions, including revenue per session and whether each user was retained.
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Model Specification: Fit a logistic regression model:
[ ex...
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