Analyze A/B test with revenue–cost tradeoffs

You receive a take‑home A/B test on a checkout change that promotes same‑day delivery. Primary metrics: conversion rate, average order value (AOV), take rate (platform % of GMV), and delivery cost per order. Data characteristics: n≈50k users/arm; right‑skewed AOV and cost; unequal variances between arms (variance ratio ≈2); 15% of orders have zero delivery cost due to promos. a) Choose and justify the correct hypothesis test(s) for each metric (e.g., Welch’s t‑test vs classic t‑test vs nonparametric/bootstrapping vs z‑test), and specify distributional assumptions you rely on and how you’ll validate them. b) Quantify net revenue impact: define and compute contribution per order = GMV×take_rate − delivery_cost, allowing delivery_cost to increase with order volume and acknowledging take_rate saturation at high discounts. Show how you’d model cost scaling (e.g., piecewise/queueing‑informed function) and diminishing take_rate, and how you’d propagate uncertainty to a final decision. c) Propose a segmentation plan (e.g., market, daypart, basket size, new vs repeat) to detect heterogeneous treatment effects; explain how you’ll control for multiplicity and avoid overfitting while still surfacing actionable segments. d) Given operational risk of manually increasing shopper supply, propose an optimization objective and constraints that balance short‑term contribution lift with service‑level metrics (SLAs, cancellation risk).