Calculate expected value for coin flips
Last updated: December 16, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the p-value.
HRT
Statistics & Math
Data Scientist
HRT
December 16, 2025Data Scientist
Phone Screen
Statistics & Math
Hard
35
6
1,905 solved
Given the following scenario about revenue per session, calculate the the p-value.
This statistics question from HRT'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
Regression analysis
Causal inference basics
Conditional probability and Bayes theorem
Bayesian vs frequentist inference
Hypothesis testing (H0, H1, p-values)
Confidence intervals and significance levels
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 design a follow-up experiment based on these results?
- How would you explain this result to a non-technical audience?
- How would you handle multiple comparisons?
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Problem Formulation
To analyze the expected revenue from a series of coin flips and calculate the p-value, we first need to define the variables involved in this scenario. Let:
- X be the number of successful outcom...
Solution Approach
- Define the null and alternative hypotheses:
- H0: The expected revenue is equal to a baseline revenue (e.g., revenue from a previous period).
- H1: The expected revenue is greater than th...
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