Confidence Interval for Fraud Loss Change | Dataford Interview Questions

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Business Context

PayWave, a digital payments company, launched a new fraud detection model on a subset of card transactions. Risk leadership wants to know how to interpret the confidence interval around the observed change in fraud loss rate before deciding on a broader rollout.

Problem Statement

Compare fraud loss rates between the old model (control) and the new model (treatment), compute a 95% confidence interval for the change in loss rate, and explain what that interval means for the business.

Given Data

Fraud loss rate is defined as the proportion of transactions that resulted in confirmed fraud loss.

Group	Transactions	Fraud-loss transactions	Observed loss rate
Control (old model)	80,000	1,040	1.30%
Treatment (new model)	82,000	902	1.10%

Use a 95% confidence level.

Requirements

Define the parameter of interest as the change in fraud loss rate: $p_{treatment} - p_{control}$ .
Compute the sample fraud loss rates for both groups.
Calculate the standard error for the difference in proportions using the unpooled formula for a confidence interval.
Construct the 95% confidence interval for the change in fraud loss rate.
State whether the interval suggests a statistically significant reduction in fraud loss.
Interpret the interval in plain business language, including what it does and does not mean.

Assumptions

Transactions were randomly assigned between control and treatment.
Each transaction outcome is independent for the purpose of this approximation.
Sample sizes are large enough for the normal approximation to hold.
Use a two-sided 95% confidence interval with critical value $z_{0.975} = 1.96$ .