Business Context
ProcureMax tracks monthly spend with key suppliers to monitor inflation risk and renegotiate contracts early. You are given two consecutive monthly cost periods for one supplier and need to quantify the change.
Problem Statement
Calculate the percentage change in average supplier cost from Period 1 to Period 2. Then estimate whether the observed increase is large relative to normal day-to-day cost variability using a confidence interval for the mean difference.
Given Data
The procurement team sampled invoice-level unit costs for the same SKU family in two consecutive months.
| Metric | Period 1 | Period 2 |
|---|
| Number of invoices | 36 | 40 |
| Mean unit cost | 48.75 | 52.16 |
| Standard deviation of unit cost | 4.20 | 4.65 |
Additional inputs:
| Parameter | Value |
|---|
| Significance level | 0.05 |
| Confidence level | 95% |
Requirements
- Compute the period-over-period percentage change in mean supplier cost.
- Compute the absolute change in mean cost.
- Estimate the standard error of the difference in means assuming independent samples.
- Construct a 95% confidence interval for the mean cost difference using a normal approximation.
- Interpret whether costs appear to have materially increased from a business perspective.
Assumptions
- Invoice samples from the two periods are independent.
- Unit costs are measured consistently across periods for the same SKU family.
- Sample sizes are large enough for a normal approximation to the sampling distribution of the mean difference.
- Ignore mix-shift effects across product subtypes; treat the reported means as directly comparable.
