Sample Size for Signup Growth Test

Business Context

PulseFit, a fitness subscription app, wants to test a new onboarding flow designed to increase paid signup conversion from landing-page visitors. Before launching the experiment, the growth team needs to know how many users are required for the test to be conclusive.

Problem Statement

Estimate the required sample size per variant for a two-arm A/B test on conversion rate. The team wants enough traffic to detect a meaningful lift with high probability while controlling false positives.

Given Data

A 12.0% relative lift on an 8.4% baseline implies a treatment conversion rate of 9.408%.

Requirements

1. Convert the relative lift into an absolute effect size.
2. State the null and alternative hypotheses.
3. Compute the approximate required sample size per group using the normal approximation for two proportions.
4. Estimate total sample size and expected test duration in weeks.
5. Briefly explain how the answer would change if the team wanted 90% power instead of 80%.

Assumptions

• Users are independently randomized at the visitor level.
• Conversion is binary and each visitor is counted once.
• The normal approximation is appropriate at this traffic scale.
• No major seasonality or product changes occur during the experiment window.
• The primary metric is signup conversion; guardrails are not part of this calculation.