Calculate probability for user retention
Last updated: November 5, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
Databricks
Statistics & Math
Data Scientist
Databricks
November 5, 2025Data Scientist
Phone Screen
Statistics & Math
Hard
45
6
4,774 solved
Given the following scenario about user conversion, calculate the the sample size needed.
This statistics question from Databricks'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
- 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
Conditional probability and Bayes theorem
Power analysis and sample size calculation
Regression analysis
Causal inference basics
Multiple testing correction (Bonferroni, FDR)
Hypothesis testing (H0, H1, p-values)
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 assumptions does this test make, and how would you validate them?
- What alternative statistical method could you use here?
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Problem Formulation
To calculate the sample size needed for user retention analysis at Databricks, we first need to define the parameters of our study. Let's denote the following:
- p1: The proportion of users retai...
Solution Approach
- Determine z-scores: For α = 0.05, is approximately 1.96. For β = 0.2, is approximately 0.84.
- Estimate p1 and p2: For example, let’s assume (60% r...
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