Calculate conditional probability for user retention
Last updated: April 16, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
DE Shaw
April 16, 202622
5
1,369 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Statistics questions at DE Shaw test your ability to reason quantitatively and design rigorous experiments. This Take-home Project question evaluates your understanding of statistical inference and its application to business decisions.
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 explain this result to a non-technical audience?
- What alternative statistical method could you use here?
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Problem Formulation
To calculate the sample size needed for assessing user retention based on revenue per session, we start by defining the parameters of our problem using statistical notation. Let:
- : the true ...
Solution Approach
- Determine the Desired Confidence Level and Margin of Error: Assuming we want a 95% confidence level, is 1.96. Let’s say we want a margin of error of 0.05.
- **Estima...
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