Business Context
FreshCart, a grocery delivery app, tested a new personalized coupon banner to increase first-order redemption. The growth team wants to know whether the observed lift is real before rolling it out to all new users.
Problem Statement
You are given results from a 10-day randomized experiment comparing the existing generic coupon banner (control) against a personalized banner (treatment). Determine whether the treatment increased coupon redemption rate.
Given Data
| Group | Sample Size | Redemptions | Redemption Rate |
|---|
| Control | 8,400 | 1,008 | 12.0% |
| Treatment | 8,100 | 1,085 | 13.4% |
Additional test settings:
| Parameter | Value |
|---|
| Significance level | 0.05 |
| Test type | Two-proportion z-test |
| Confidence level | 95% |
Requirements
- State the null and alternative hypotheses.
- Compute the sample redemption rates and the observed lift.
- Calculate the pooled proportion and standard error under the null.
- Compute the z-statistic and two-sided p-value.
- Construct a 95% confidence interval for the difference in redemption rates.
- Decide whether the result is statistically significant at α=0.05.
- Explain what the result means for the rollout decision.
Assumptions
- Users were randomly assigned to control and treatment.
- Each user is counted once and outcomes are independent.
- Sample sizes are large enough for the normal approximation.
- No major traffic-quality changes occurred during the 10-day test.
