Calculate probability for user retention

Last updated: July 22, 2025

Quick Overview

Given the following scenario about user conversion, calculate the the p-value.

Citadel

Statistics & Math

Data Scientist

Citadel

July 22, 2025

Data Scientist

Technical Screen

Statistics & Math

Medium

103

217 solved

Given the following scenario about user conversion, calculate the the p-value.

This statistics question from Citadel'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

Bayesian vs frequentist inference

Causal inference basics

Multiple testing correction (Bonferroni, FDR)

Conditional probability and Bayes theorem

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

How would you design a follow-up experiment based on these results?
What assumptions does this test make, and how would you validate them?
What if the sample size is very small?

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Sample Answer

Problem Formulation

To calculate the p-value for user retention, we first need to define our hypotheses:

Null Hypothesis (H0): There is no difference in user retention rates between the control group and the treat...

Solution Approach

Gather Data: Suppose we have:
- Control group: $n_1 = 1000$ , $r_1 = 200$ (retention rate $p_1 = 0.2$ )
- Treatment group: $n_2 = 1000$ , $r_2 = 300$ (retention rate ( p...

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