Calculate variance for user retention
Last updated: September 7, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the p-value.
Zoom
Statistics & Math
Data Scientist
Zoom
September 7, 2025Data Scientist
Take-home Project
Statistics & Math
Easy
157
5
2,225 solved
Given the following scenario about revenue per session, calculate the the p-value.
This statistics question from Zoom's Take-home Project 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
- 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
Central Limit Theorem
Bayesian vs frequentist inference
Probability distributions
Conditional probability and Bayes theorem
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
- What if the sample size is very small?
- What assumptions does this test make, and how would you validate them?
- How would you explain this result to a non-technical audience?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To calculate the p-value for user retention based on revenue per session, we need to define our null hypothesis and alternative hypothesis .
- Null Hypothesis (H0): There is n...
Solution Approach
- Collect Data: Gather sample data on user retention rates and revenue per session.
For example, suppose we have the following data:
- Revenue per session: [20, 25, 30, 35, 40]
- User re...
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