## Problem You have aerial-drone data that records the **2D turning trajectories** of vehicles passing through multiple intersections. Each trajectory corresponds to one vehicle executing a turn (e.g., left or right) within an intersection. Some trajectories are from **Waymo autonomous vehicles**, and the rest are from **other vehicles** (human-driven and/or other fleets). You want to quantify whether **Waymo’s turning behavior differs** from the population of all other vehicles. ### Data (assume) Each observed turn is a trajectory with timestamps: - `intersection_id` - `vehicle_type` (Waymo vs Other) - `turn_type` (left/right/straight, if available) - `t` (time) - `x(t), y(t)` (position in a local intersection coordinate frame) Optionally derived signals (from smoothing/finite differences): - speed `v(t)`, heading `θ(t)`, curvature `κ(t)`, acceleration `a(t)` ### Tasks 1. **Define a statistical approach** to test/quantify whether Waymo trajectories differ from other vehicles. - What trajectory representation / features would you use? - What distributional assumptions (if any) would you make? - What hypothesis test or model would you use? - What effect size would you report? 2. **Follow-up (traffic volume differs by intersection):** Intersections have different traffic volumes and potentially different driving patterns. - How would you adjust your analysis so differences aren’t confounded by intersection-level factors (including traffic volume)? - What model or design would you use to compare Waymo vs Other fairly across intersections? State key assumptions, pitfalls, and how you’d validate them.