Calculate expected value for click-through rates
Last updated: January 26, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the p-value.
Grubhub
Statistics & Math
Data Scientist
Grubhub
January 26, 2026Data Scientist
Onsite
Statistics & Math
Medium
37
5
2,453 solved
Given the following scenario about revenue per session, calculate the the p-value.
Grubhub 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
Causal inference basics
Power analysis and sample size calculation
Central Limit Theorem
Probability distributions
Regression analysis
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 alternative statistical method could you use here?
- How would you handle multiple comparisons?
- How would you explain this result to a non-technical audience?
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Problem Formulation
In this scenario, we want to analyze the click-through rates (CTR) for Grubhub's platform to evaluate the effectiveness of a new marketing strategy. Let's denote:
- : the number of sessions (cl...
Solution Approach
- Define the Hypotheses:
- Null Hypothesis (H0): The new strategy has no effect on CTR ().
- Alternative Hypothesis (H1): The new strategy increases CTR (( p_{new} >...
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