Calculate variance for user retention
Last updated: October 13, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the p-value.
Cruise
Statistics & Math
Data Scientist
Cruise
October 13, 2025Data Scientist
Technical Screen
Statistics & Math
Medium
6
12
4,806 solved
Given the following scenario about revenue per session, calculate the the p-value.
Cruise values data-driven decision making. This Technical Screen 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
Confidence intervals and significance levels
Conditional probability and Bayes theorem
Power analysis and sample size calculation
Probability distributions
Regression analysis
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?
- How would you handle multiple comparisons?
- How would you design a follow-up experiment based on these results?
- What assumptions does this test make, and how would you validate them?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To analyze user retention in relation to revenue per session at Cruise, we first need to set up our mathematical framework.
Let represent the revenue per session, and let be the bina...
Solution Approach
- Data Collection: Gather data on revenue per session and corresponding user retention rates.
- Group Data: Divide the data into categories (e.g., low, medium, high revenue per session). 3...
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