Business Context

StreamCart, a grocery delivery app, wants to test a faster checkout flow. The product manager argues for shipping after one week to increase experimentation velocity, while the data science team wants enough sample size to maintain statistical power.

Problem Statement

You need to quantify the trade-off between running a short experiment and waiting for a statistically rigorous result. Assume the team cares about detecting a meaningful lift in checkout conversion.

Given Data

The one-week result implies treatment conversion of 19.3% versus 18.0% in control.

Requirements

1. Compute the required sample size per group to detect the target 1.5 percentage point lift with 80% power.
2. Convert that sample size into the approximate number of days needed at the given traffic level.
3. Using the one-week observed data, run a two-proportion z-test.
4. Compute a 95% confidence interval for the observed lift.
5. Decide whether shipping after one week is justified.
6. Explain how you would balance experimentation speed and statistical rigor in practice.

Assumptions

• Users are independently randomized at the user level.
• No major novelty effect or traffic-quality shift occurs during the test.
• The normal approximation for proportions is valid.
• Use a two-sided test.