Design and power an A/B test

You plan to launch a targeting model via email: treat = users above a score threshold receive an email; control = withheld. (1) Choose a primary success metric and two guardrails (e.g., unsubscribe rate, complaint rate) and justify them. (2) Given a baseline 7-day purchase rate of 5% and an expected relative lift of 8%, compute the minimum per-arm sample size for a two-sided test with α=0.05 and 80% power; show your formulas/assumptions (continuity-corrected normal approximation is fine). (3) Propose a ramp plan with sequential monitoring that controls type-I error (e.g., group-sequential or alpha-spending); specify interim looks and stopping rules. (4) Describe pre-experiment checks (randomization, covariate balance, holdout contamination) and how you'd handle interference and seasonality around weekends. (5) If legal or traffic constraints prevent pure A/B, propose a credible quasi-experimental design (e.g., regression discontinuity on the score threshold or staggered difference-in-differences), and list the assumptions you would test and the plots you'd include in your slides.