Calculate conditional probability for user retention
Last updated: May 19, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
Apple
May 19, 20267
13
3,134 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Apple values data-driven decision making. This Onsite 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
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 design a follow-up experiment based on these results?
- What if the sample size is very small?
- What assumptions does this test make, and how would you validate them?
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Browse Statistics QuestionsSample Answer
Problem Formulation
We want to determine the sample size required to estimate the conditional probability of user retention for Apple, given a specific revenue per session. Let denote revenue per session, and ( ...
Solution Approach
To calculate the sample size needed for estimating , we need to use the formula for sample size in estimating proportions: [ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \cdot (p(1-p))}{d^2}...
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