Calculate conditional probability for click-through rates
Last updated: September 14, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
Atlassian
September 14, 202564
4
2,289 solved
Given the following scenario about user conversion, calculate the the sample size needed.
Statistics questions at Atlassian test your ability to reason quantitatively and design rigorous experiments. This Technical Screen question evaluates your understanding of statistical inference and its application to business decisions.
What the Interviewer Expects
- Derive results from first principles when needed
- Handle complex scenarios with multiple interacting variables
- Design experiments that account for real-world complications
- Discuss advanced topics: Bayesian methods, causal inference, resampling
- Connect statistical concepts to business decision-making
- Identify subtle errors in reasoning (Simpson's paradox, survivorship bias)
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?
- How would you design a follow-up experiment based on these results?
- What if the sample size is very small?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To calculate the sample size needed for estimating click-through rates (CTR) with a specified level of confidence and margin of error, we can model the problem using conditional probability.
Let ( ...
Solution Approach
- Define the parameters:
- Desired confidence level (e.g., 95%) →
- Estimated CTR (assume based on historical data)
- Desired margin of error ( E ...
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