Business Context
QuickCart, a grocery delivery app, launched a new driver-routing algorithm in one city. The operations team believes the average delivery time is unchanged, but variability may have increased, which would make service less predictable.
Problem Statement
Assess whether the new routing algorithm changed the variance of delivery times compared with the old system. This is a variance analysis problem: the goal is not to compare means, but to determine whether delivery-time consistency has materially changed.
Given Data
A random sample of completed deliveries was taken before and after the rollout.
| Group | Sample Size | Sample Mean (minutes) | Sample Standard Deviation (minutes) | Sample Variance |
|---|
| Old routing | 40 | 31.8 | 4.5 | 20.25 |
| New routing | 35 | 33.1 | 6.2 | 38.44 |
Use a two-sided test at significance level α=0.05.
Requirements
- State the null and alternative hypotheses for equality of variances.
- Compute the test statistic for comparing two variances.
- Find the rejection region or p-value using the appropriate distribution.
- Decide whether the variance difference is statistically significant.
- Quantify how much larger the new-routing variance is relative to the old-routing variance.
- Briefly explain what the result implies for operations.
Assumptions
- Delivery times in each group are independent random samples.
- Delivery times are approximately normally distributed in each period.
- The samples are representative of typical operating conditions.
- The question focuses on variance stability, not causal attribution beyond this city rollout.
