Calculate expected value for coin flips

Last updated: May 20, 2026

Quick Overview

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

Amazon

Statistics & Math

Data Scientist

Amazon

May 20, 2026

Data Scientist

Take-home Project

Statistics & Math

Medium

4,740 solved

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

This statistics question from Amazon's Take-home Project 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

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

Bayesian vs frequentist inference

Probability distributions

Hypothesis testing (H0, H1, p-values)

Multiple testing correction (Bonferroni, FDR)

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 assumptions does this test make, and how would you validate them?
What alternative statistical method could you use here?
What if the sample size is very small?
How would you handle multiple comparisons?

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Sample Answer

Problem Formulation

To determine the sample size needed for calculating the expected revenue per session from coin flips, we need to formalize our problem. Let:

$p$ : the probability of getting heads (success), whic...

Solution Approach

To calculate the required sample size $n$ , we can use the formula: $n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right)$ Where:

$Z$ is the Z-value corresponding to the desired confi...

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