Business Context

StreamCart, a grocery delivery app, wants to test a new homepage layout intended to increase first-order conversion. The product manager asks how to design control and treatment groups so the experiment is valid and adequately powered.

Problem Statement

Design the experiment and quantify whether the proposed sample split is sufficient to detect the target lift. Assume the current conversion rate is 18.0%, and the team wants to detect an absolute lift of 1.5 percentage points with 80% power at a 5% significance level.

Given Data

Requirements

1. Define the control and treatment groups and explain the randomization unit.
2. State the null and alternative hypotheses for the conversion metric.
3. Calculate the required sample size per group for a two-sided two-proportion test.
4. Determine whether the planned 20,000 total users are enough.
5. Briefly explain why a 50/50 split is typically preferred here.
6. List key design safeguards to avoid bias in the control and treatment groups.

Assumptions

• Randomization is at the user level, and each user appears once.
• Users are independently assigned to groups.
• No major seasonality or marketing shocks occur during the test window.
• The primary metric is binary conversion, so a two-proportion normal approximation is appropriate.