Design and power an incentive experiment

Design an experiment to assess whether offering a bonus—such as cash or queue priority—raises the proportion of candidates who have completed paperwork and then complete their first action within 14 days. Define eligibility and exclusions; the randomization unit; treatment arms (control, bonus-now, bonus-after-first-action, staged bonus); stratification to distinguish bonus-dependent from intrinsically motivated users; primary and secondary metrics plus guardrails (quality, fraud, downstream retention); how to handle noncompliance, spillovers, and interference; and stopping rules and decision criteria. Calculate the minimum sample size per arm needed to detect a +3 percentage-point increase over a 20% baseline with 90% power and α=0.05 using a two-proportion z-test; show the formula and a numeric result. Explain when benefits should be rolled out broadly versus targeted narrowly, based on heterogeneous treatment effects.

Overview: This question tests skills in experimental design, causal inference, A/B testing, and statistical power calculation, including defining eligibility, the unit of randomization, treatment arms, stratification, metric selection with guardrails, handling noncompliance and interference, and interpreting heterogeneous treatment effects.