Calculate variance for user retention

Last updated: January 25, 2026

Quick Overview

Given the following scenario about user conversion, calculate the the sample size needed.

Statistics & Math

Data Scientist

January 25, 2026

Data Scientist

Phone Screen

Statistics & Math

Hard

60 solved

Given the following scenario about user conversion, calculate the the sample size needed.

This statistics question from Pinterest's Phone 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

Derive results from first principles when needed
Handle complex scenarios with multiple interacting variables
Design experiments that account for real-world complications
Discuss advanced topics: Bayesian methods, causal inference, resampling
Connect statistical concepts to business decision-making
Identify subtle errors in reasoning (Simpson's paradox, survivorship bias)

Key Topics to Cover

Regression analysis

Confidence intervals and significance levels

Bayesian vs frequentist inference

Probability distributions

Causal inference basics

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 alternative statistical method could you use here?
How would you design a follow-up experiment based on these results?

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Sample Answer

Problem Formulation

To calculate the sample size needed to evaluate user retention on Pinterest, we need to define several key parameters: the expected retention rate, the desired confidence level, the margin of error, a...

Solution Approach

To calculate the required sample size (n), we can use the formula for sample size determination for proportions:

$n = \frac{Z^2 \cdot p(1-p)}{E^2}$

Where:

$Z$ is the Z-score corresponding ...

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