Design an A/B for ATO rule

Experiment design case: PayPal/Venmo wants to launch a new real-time ATO rule that blocks high-risk transfers. Design and analyze an online experiment to estimate net business impact. Constraints and inputs: (1) Randomization unit must avoid cross-over: choose user_id vs. transaction-level; justify with interference risks (recipients can be common). (2) Baselines: weekly fraud base rate on transfers p0 = 0.0012, average fraudulent loss per incident L_f = $200, expected relative reduction = 20%; legitimate block cost C_fp = $1.50 per blocked legit transfer; expected block rate under treatment = 1.0% of legit transfers. (3) Traffic: 10M transfers/week, average 5 transfers per active user/week; ICC (cluster at user) = 0.02, average cluster size m = 5. (4) Guardrails: auth success rate, dispute rate within 7 days, P95 time-to-pay. (5) Stats: two-sided alpha 0.05, power 0.80; allow sequential monitoring (daily) with alpha spending; require pre-registration and an A/A test. Tasks: A) Choose randomization unit and explain spillover/contamination mitigations (e.g., recipient or graph clusters). B) Compute the minimum per-arm sample size (transfers) for detecting a 20% relative drop in fraud rate using a two-sample proportion Z-test; then inflate by the design effect DE = 1 + (m-1)*ICC. Show formulas and numeric results. C) Convert the detectable effect into expected weekly net dollars using: Net = (Fraud prevented * L_f) - (Incremental legit blocks * C_fp); state any additional assumptions you need and bound the estimate. D) Define primary, secondary, and guardrail metrics with precise denominators; specify slicing (e.g., by device novelty, account age). E) Propose a ramp plan and stopping rules under group sequential design (e.g., Pocock or O'Brien–Fleming), and how you’ll monitor production for post-launch drift.