Calculate probability for click-through rates
Last updated: September 19, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
Citadel
September 19, 2025297
10
2,268 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Citadel 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
- 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 handle multiple comparisons?
- What alternative statistical method could you use here?
- What if the sample size is very small?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To determine the sample size needed to estimate the click-through rate (CTR) with a specified level of confidence and margin of error, we first define the parameters involved. Let:
- : estimat...
Solution Approach
- Estimate the click-through rate (p): For this example, we'll assume an estimated CTR of 0.05 (5%).
- Set the margin of error (E): For a margin of error of 0.01 (1%).
- **Determine Z-score...
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