Business Context
FinServe tracks daily handling time for its customer support team. The operations manager is less concerned with the average handle time than with consistency, because high variability makes staffing and service-level planning unreliable.
Problem Statement
A process change was introduced to standardize call routing. You need to determine whether the new process reduced variability in daily average handle time.
Given Data
The team measured daily average handle time (in minutes) for 10 business days before and 10 business days after the change.
| Period | Sample Size | Sample Mean (min) | Sample Variance (min2) |
|---|
| Before change | 10 | 8.4 | 2.25 |
| After change | 10 | 8.1 | 0.81 |
Use a one-sided variance test at significance level α=0.05.
Requirements
- Explain why variance analysis matters in this business setting.
- State the null and alternative hypotheses for testing whether variance decreased.
- Compute the test statistic using the sample variances.
- Determine the critical value or p-value using the appropriate distribution.
- Conclude whether the reduction in variability is statistically significant.
- Briefly interpret the operational impact of lower variance, even if the mean changed only slightly.
Assumptions
- Daily observations are independent within each period.
- Daily average handle times are approximately normally distributed.
- The two samples are from comparable operating conditions aside from the routing change.
