Calculate variance for A/B test results

Last updated: November 10, 2025

Quick Overview

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

Tesla

Statistics & Math

Data Scientist

Tesla

November 10, 2025

Data Scientist

Technical Screen

Statistics & Math

Medium

4,403 solved

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

This statistics question from Tesla's Technical 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

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

Conditional probability and Bayes theorem

Hypothesis testing (H0, H1, p-values)

Confidence intervals and significance levels

Multiple testing correction (Bonferroni, FDR)

Bayesian vs frequentist inference

Probability distributions

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?
How would you explain this result to a non-technical audience?
What alternative statistical method could you use here?

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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 (control group A and treatment group B), we need to define the following parameters:

**Effect S...

Solution Approach

The formula for calculating the required sample size for each group in an A/B test is given by:

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

Wh...

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