Design promo experiment and explain correlation

You work on a ride-hailing marketplace (drivers + riders). Answer the following analytics and experimentation questions. ## 1) Interpret a surprising correlation You observe in data that **driver time-to-arrive at the rider pickup location** is **positively correlated** with **rider order acceptance / completion rate** (i.e., longer arrival time is associated with higher acceptance). ### Tasks - Clarify and define the exact time interval (e.g., request → driver assignment, assignment → driver arrival, driver arrival → pickup, etc.). - Provide multiple plausible explanations (including confounding and selection effects) for why this positive correlation could appear. - Propose analyses (or an experiment) to determine whether *longer arrival time causes higher acceptance*, or whether the relationship is spurious. ## 2) Design an experiment for a threshold discount A new promotion is proposed: - If a trip’s **pre-discount fare ≥ T** (a threshold), the rider receives **20% off** that trip. ### Tasks 1. Design an experiment to estimate the causal impact of the promotion. - Specify unit of randomization (rider, request, city/time), eligibility rules, duration, and how to handle interference in a two-sided marketplace. 2. Choose metrics: - Primary success metric for the **platform**. - Diagnostic/secondary metrics for **riders**, **drivers**, and marketplace health. - Guardrail metrics (fraud, cancellations, ETAs, etc.). 3. A teammate suggests analyzing effect by grouping trips by realized fare buckets (e.g., $10–$20, $20–$30) and comparing treatment vs control within each bucket. - Is this valid? Why/why not? - If not valid, propose better approaches (e.g., alternative stratification, causal methods, or quasi-experimental designs). State any assumptions you make.