Calculate variance for click-through rates
Last updated: December 26, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
JPMorgan
December 26, 202548
6
4,428 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
JPMorgan 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
- What assumptions does this test make, and how would you validate them?
- How would you design a follow-up experiment based on these results?
- How would you handle multiple comparisons?
- How would you explain this result to a non-technical audience?
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Problem Formulation
To calculate the variance for click-through rates (CTR) and determine the sample size needed, we need to set up a mathematical framework. Let be the probability of a user clicking on a link (C...
Solution Approach
- Determine the parameters: Choose a confidence level (e.g., 95%), which corresponds to a Z-score of approximately 1.96.
- Estimate the CTR: Assume a preliminary click-through rate based o...
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