You are the lead data scientist embedded with a joint military logistics task force responsible for convoy operations across multiple regions. The commander is deciding whether to change routing policy and allocate additional electronic countermeasure (ECM) equipment. A dashboard shows that the weekly rate of roadside incidents per 1,000 convoy-miles dropped after a new route-planning protocol was introduced, but the commander is skeptical: “Is this real improvement or just random fluctuation?”
You have 16 weeks of data: 8 weeks before the protocol and 8 weeks after. The number of convoy-miles varies week to week, so you should compare rates, not raw counts.
Quantify whether the post-change incident rate is meaningfully lower than the pre-change rate.
Build a commander-friendly explanation that communicates: (a) the size of the effect, (b) uncertainty, and (c) what decision the data supports.
You may assume incidents are rare relative to miles traveled and can be modeled as a Poisson process with exposure (miles). Treat the two periods as independent.
| Period | Weeks | Total Convoy Miles | Total Incidents | Observed Rate (per 1,000 miles) |
|---|---|---|---|---|
| Pre-protocol | 8 | 412,000 | 52 | 0.1262 |
| Post-protocol | 8 | 398,000 | 33 | 0.0829 |
Use a one-sided test at α = 0.05 (we only care if the rate decreased).