Calculate probability for A/B test results

Last updated: May 19, 2026

Quick Overview

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

Goldman Sachs

Statistics & Math

Data Scientist

Goldman Sachs

May 19, 2026

Data Scientist

Phone Screen

Statistics & Math

Medium

1,389 solved

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

Statistics questions at Goldman Sachs test your ability to reason quantitatively and design rigorous experiments. This Phone Screen question evaluates your understanding of statistical inference and its application to business decisions.

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

Power analysis and sample size calculation

Multiple testing correction (Bonferroni, FDR)

Hypothesis testing (H0, H1, p-values)

Central Limit 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?
What assumptions does this test make, and how would you validate them?
What alternative statistical method could you use here?
How would you explain this result to a non-technical audience?

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Sample Answer

Problem Formulation

To calculate the sample size required for an A/B test on revenue per session, we need to define our hypotheses and the parameters of the test. Let:

$H_0$ : There is no difference in average reve...

Solution Approach

The sample size $n$ for each group can be calculated using the formula:

$n = \left( \frac{(Z_{\alpha/2} + Z_{\beta}) \cdot \sigma}{\delta} \right)^2$

Where:

$Z_{\alpha/2}$ is the z-sc...

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