Delivery times under old and new routing (independent samples)

What it is good for

• Run a Welch two-sample t-test and a Mann–Whitney test and interpret them.
• Explain why independent samples need more data than a paired design for the same effect.
• Check skewness and unequal spread before choosing a test.

Methods: Welch t-test, pooled t-test, Mann–Whitney U test, confidence interval for a difference in means, power.

Data quality notes

• Delivery times are right-skewed (log-normal variation).
• The true saving is 3 minutes, but with this sample size the difference may not be statistically significant — a teachable contrast with the paired data.
• No missing values.

Provenance and licence

Each delivery's time = route-level average (as in delivery_process: ≈ 18 + 0.25·distance + 0.6·stops) − 3 minutes under the new system, multiplied by log-normal delivery-to-delivery variation (sd 0.25 on the log scale), rounded to 0.1 minute. Old-system deliveries come from the four weeks before the change, new-system deliveries from the four weeks after.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241118). It does not describe real people or organisations; any resemblance is coincidental.