Business Context
QuickCart, a grocery delivery company, changed picker routing logic in one warehouse. Operations cares less about the average fulfillment time than about consistency, because high variability causes missed delivery windows.
Problem Statement
You need to assess whether the new routing process changed the variance of order fulfillment time compared with the old process.
Given Data
A random sample of completed orders was taken before and after the routing change.
| Group | Sample Size | Sample Mean (min) | Sample Variance (min^2) |
|---|
| Old routing | 25 | 31.8 | 36.0 |
| New routing | 20 | 30.9 | 16.0 |
Use a two-sided test at significance level 0.05.
Requirements
- State the null and alternative hypotheses for equality of variances.
- Compute the F-statistic using the larger sample variance in the numerator.
- Determine the two-sided p-value using the appropriate F distribution degrees of freedom.
- Decide whether the variance changed significantly.
- Briefly explain how this variance result should influence the operational decision.
Assumptions
- Fulfillment times in each group are independent.
- Samples are random and representative of the same warehouse conditions.
- Fulfillment times are approximately normally distributed, so the F-test for variances is appropriate.
- The goal is to test variance, not mean difference.
