Calculate expected value for user retention
Last updated: March 12, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the p-value.
Spotify
Statistics & Math
Data Scientist
Spotify
March 12, 2026Data Scientist
Take-home Project
Statistics & Math
Easy
8
8
4,740 solved
Given the following scenario about revenue per session, calculate the the p-value.
Spotify values data-driven decision making. This Take-home Project 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
- State the correct formula or theorem with clear definitions
- Apply the concept to the given scenario step by step
- Interpret the result in plain language
- Identify assumptions and when they might be violated
Key Topics to Cover
Multiple testing correction (Bonferroni, FDR)
Conditional probability and Bayes theorem
Hypothesis testing (H0, H1, p-values)
Causal inference basics
Power analysis and sample size calculation
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?
- How would you design a follow-up experiment based on these results?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To analyze user retention for Spotify based on revenue per session, we first need to set up our hypothesis tests. We will define:
- Null Hypothesis (H0): There is no significant difference in use...
Solution Approach
- Data Collection: Collect retention rates and revenue per session data before and after the change.
- Calculate Proportions: Calculate the retention rates for both periods:
- ( p_1 = r...
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