Calculate expected value for coin flips
Last updated: November 2, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
Airbnb
November 2, 20254
4
2,188 solved
Given the following scenario about user conversion, calculate the the sample size needed.
This analytics question from Airbnb's Technical Screen tests your ability to think critically about data. The interviewer expects you to consider confounding variables, selection bias, and the difference between correlation and causation.
What the Interviewer Expects
- Define clear success metrics aligned with business goals
- Propose a basic experimental design with control and treatment groups
- Interpret results correctly and draw reasonable conclusions
- Identify obvious confounding variables
Key Topics to Cover
How to Approach This
- Define success metrics carefully. A good metric is measurable, actionable, and aligned with business goals.
- Run experiments long enough to account for novelty effects and weekly seasonality.
- Use funnel analysis to identify where users drop off for maximum optimization impact.
- Segment results by key dimensions (platform, country, user cohort) to catch hidden patterns.
- Consider network effects and interference between treatment and control groups.
Possible Follow-up Questions
- How would you handle interference between treatment and control?
- What if you discover a bug in the logging during the experiment?
- What would you do if a stakeholder wants to end the experiment early because initial results look good?
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Problem Setup
To determine the expected value for coin flips regarding user conversion on Airbnb, we need to define the specific analytical question: **What is the sample size required to confidently detect a signi...
Methodology
To calculate the required sample size for our experiment, we can use the following formula for a two-proportion z-test:
[ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \times (p_1(1 - p_1) + p_2(1 - p_2)...
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