Calculate conditional probability for A/B test results

Last updated: September 11, 2025

Quick Overview

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

Dropbox

Statistics & Math

Data Scientist

Dropbox

September 11, 2025

Data Scientist

Technical Screen

Statistics & Math

Medium

348

3,449 solved

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

Dropbox values data-driven decision making. This Technical Screen 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

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

Probability distributions

Causal inference basics

Central Limit Theorem

Hypothesis testing (H0, H1, p-values)

Multiple testing correction (Bonferroni, FDR)

Power analysis and sample size calculation

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?
What if the sample size is very small?
How would you design a follow-up experiment based on these results?

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Sample Answer

Problem Formulation

To determine the sample size needed for an A/B test comparing revenue per session between two groups (A and B), we start by defining the following parameters:

Null Hypothesis (H0): There is no...

Solution Approach

We will use the formula for sample size calculation for comparing two means:

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

Where:

$n$ is the sample size per gro...

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