Business Context

StreamCart, a grocery delivery app, tested a new personalized reorder widget on the home screen. The feature appears to increase 7-day reorder conversion slightly, and the PM wants to know whether statistical significance alone is enough to ship.

Problem Statement

You need to evaluate whether the observed lift is statistically significant, quantify the uncertainty, and decide whether the feature should be launched given a small implementation cost and potential UX risk.

Given Data

The experiment ran for 21 days with user-level randomization.

Additional business inputs:

Requirements

1. State the null and alternative hypotheses for a two-sided test.
2. Use a two-proportion z-test to determine whether the lift is statistically significant.
3. Compute the absolute lift, relative lift, z-statistic, p-value, and a 95% confidence interval for the difference in conversion rates.
4. Estimate the expected monthly incremental gross profit if the observed lift holds at full rollout.
5. Based on both statistical and practical significance, recommend whether StreamCart should ship the feature.

Assumptions

• Randomization was valid and there is no sample ratio mismatch.
• Each user appears once in the analysis.
• The observed treatment effect scales approximately linearly to full rollout.
• No major guardrail metric regressions were observed outside this primary metric.