Calculate expected value for A/B test results
Last updated: May 3, 2026
Quick Overview
Given the following scenario about user conversion, calculate the the p-value.
Zillow
Statistics & Math
Data Scientist
Zillow
May 3, 2026Data Scientist
Phone Screen
Statistics & Math
Hard
44
7
2,927 solved
Given the following scenario about user conversion, calculate the the p-value.
This statistics question from Zillow's Phone Screen tests your ability to apply mathematical reasoning to practical problems. The interviewer expects precise definitions, correct methodology, and awareness of assumptions and limitations.
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
Bayesian vs frequentist inference
Causal inference basics
Confidence intervals and significance levels
Hypothesis testing (H0, H1, p-values)
Probability distributions
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
- What if the sample size is very small?
- How would you explain this result to a non-technical audience?
- How would you design a follow-up experiment based on these results?
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Browse Statistics QuestionsSample Answer
Problem Formulation
In this A/B test scenario, we aim to evaluate user conversion rates between two groups: Group A (the control group) and Group B (the variant). Let:
- : Conversion rate for Group A.
- ( p_B ...
Solution Approach
- Data Collection: Gather the number of conversions and sample sizes for both groups. For instance, let:
- Group A: 100 conversions out of 1000 users.
- Group B: 120 conversions out of 1000...
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