Two-Sample t-Test: Did Switching Carriers Really Improve Delivery Times?

The Scenario

FlowBridge Distribution Co. is a mid-sized e-commerce fulfillment company managing over 50,000 parcel shipments per month across the Southwest region. Six months ago, the operations leadership team made a critical decision: they switched their primary regional delivery partner from their long-standing provider, Carrier A, to a newer logistics company, Carrier B. Carrier B had pitched faster last-mile delivery windows, competitive pricing, and superior real-time tracking. The transition affected roughly 40% of FlowBridge's total outbound volume. To evaluate performance, the logistics analytics team carefully logged delivery time data — 120 shipments processed under Carrier A (from the six months prior to the switch) and 95 shipments processed under Carrier B (from the six months post-switch).

The Statistical Challenge

At first glance, the numbers look promising: Carrier A averaged approximately 5.2 days from dispatch to customer doorstep, while Carrier B averaged around 4.6 days — a difference of roughly half a day. But the operations team is skeptical. Delivery times naturally vary due to weather events, regional traffic, package volume spikes, and customer address complexity. The real question is: is this 0.6-day difference a genuine, reliable improvement — or could it simply be the result of random sampling variation? You've been brought in as the data analyst to apply a proper statistical test, move beyond gut feel, and determine whether the observed difference is statistically meaningful.

What's at Stake

FlowBridge's contract renewal negotiation with Carrier B opens in 30 days. If your statistical analysis confirms a significant improvement in delivery times, leadership is prepared to expand Carrier B's allocation to 80% of all regional shipments — a committed annual contract worth $1.2 million. If the evidence is inconclusive, they'll maintain a cautious hybrid model and continue monitoring. Your analysis will not sit in a slide deck — it will directly inform a procurement decision. Getting this right matters.