Calculate probability for user retention

Last updated: October 5, 2025

Quick Overview

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

Dropbox

Statistics & Math

Data Scientist

Dropbox

October 5, 2025

Data Scientist

Technical Screen

Statistics & Math

Medium

2,075 solved

Given the following scenario about user conversion, 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

Conditional probability and Bayes theorem

Power analysis and sample size calculation

Confidence intervals and significance levels

Probability distributions

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

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

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Sample Answer

Problem Formulation

To determine the sample size needed for calculating user retention at Dropbox, we will use the following framework:

Define the Parameters:
- Let $p_0$ be the current retention rate of u...

Solution Approach

We will apply the sample size formula step-by-step:

Calculate $Z_{\alpha/2}$ : For $\alpha = 0.05$ , $Z_{0.025} \approx 1.96$ .
Calculate $Z_{\beta}$ : For a power of 0.80, ...

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