Business Context

StreamCart is testing a new signup page intended to increase free-trial starts. The product manager wants to know how long the experiment must run before the team can reasonably expect to detect a meaningful lift with statistical significance.

Problem Statement

Estimate the required sample size and runtime for a two-arm A/B test on conversion rate, then check whether the currently observed data are already statistically significant.

Given Data

The business defines success as detecting at least a 10% relative lift over the baseline conversion rate.

Requirements

1. Convert the relative MDE into an absolute treatment conversion rate.
2. Compute the required sample size per group for a two-sided two-proportion test.
3. Convert that sample size into the minimum experiment runtime in days.
4. Using the current 10-day data, run a two-proportion z-test.
5. Compute a 95% confidence interval for the observed lift.
6. State whether the test should stop now or continue.

Assumptions

• Users are independently randomized at the user level.
• Conversion is binary and each user is counted once.
• Daily traffic is stable and evenly split.
• Normal approximation is appropriate because sample sizes are large.