Calculate conditional probability for click-through rates
Last updated: May 1, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the p-value.
LinkedIn
Statistics & Math
Data Scientist
Data Scientist
Onsite
Statistics & Math
Hard
10
5
801 solved
Given the following scenario about revenue per session, calculate the the p-value.
LinkedIn 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
- 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
Confidence intervals and significance levels
Bayesian vs frequentist inference
Probability distributions
Power analysis and sample size calculation
Conditional probability and Bayes theorem
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 explain this result to a non-technical audience?
- What alternative statistical method could you use here?
- What assumptions does this test make, and how would you validate them?
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Problem Formulation
To calculate the p-value for click-through rates (CTR) in this scenario, we need to establish the variables involved. Let's define:
- Null Hypothesis (H0): There is no significant difference in t...
Solution Approach
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Calculate the sample proportions:
- p_A = 200 / 1000 = 0.20
- p_B = 300 / 1200 = 0.25
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Calculate the pooled proportion (p):
- p = (200 + 300) / (1000 + 1200) = (500) / (2200) = ...
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