Calculate probability for coin flips

Last updated: April 12, 2026

Quick Overview

Given the following scenario about revenue per session, calculate the the sample size needed.

Cockroach Labs
Statistics & Math
Data Scientist
Cockroach Labs
April 12, 2026
Data Scientist
Take-home Project
Statistics & Math
Easy

6

8

1,582 solved


Given the following scenario about revenue per session, calculate the the sample size needed.

Cockroach Labs values data-driven decision making. This Take-home Project 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
  • State the correct formula or theorem with clear definitions
  • Apply the concept to the given scenario step by step
  • Interpret the result in plain language
  • Identify assumptions and when they might be violated
Key Topics to Cover
Regression analysis
Central Limit Theorem
Multiple testing correction (Bonferroni, FDR)
Probability distributions
Causal inference basics
How to Approach This
  1. Define your hypotheses (H0 and H1) clearly before performing any test.
  2. Calculate required sample size BEFORE running an experiment, using power analysis.
  3. Remember the Central Limit Theorem: sample means become approximately normal with large n.
  4. Watch for Simpson's paradox. Always segment data by key dimensions.
  5. 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?
  • What assumptions does this test make, and how would you validate them?
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Sample Answer
Problem Formulation

To determine the sample size needed to estimate the effect of revenue per session based on coin flips (which we will treat as a binary outcome), we can use the formula for sample size in the context o...

Solution Approach
  1. Determine Z-score: For a 95% confidence level, Z=1.96Z = 1.96.
  2. Estimate Proportion pp: Assume based on historical data that 60% of sessions generate revenue (i.e., p=0.6p = 0.6). 3...

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