Business Context
FinMate changed its customer support workflow and wants to know whether the post-launch increase in Net Promoter Score (NPS) reflects a real improvement or just sampling noise.
Problem Statement
NPS is defined as the percentage of promoters minus the percentage of detractors, where promoters are respondents scoring 9-10 and detractors are respondents scoring 0-6. Determine whether the change in NPS from the pre-launch survey to the post-launch survey is statistically meaningful.
Given Data
| Period | Total Responses | Promoters | Passives | Detractors | NPS |
|---|
| Before redesign | 1,200 | 540 | 360 | 300 | 20.0 |
| After redesign | 1,350 | 675 | 351 | 324 | 26.0 |
Use a two-sided test with significance level 0.05.
Requirements
- State the null and alternative hypotheses for the change in NPS.
- Compute promoter and detractor proportions in each period.
- Estimate the standard error of NPS for each period using the variance of an NPS-coded variable where promoter = 1, passive = 0, detractor = -1.
- Compute the standard error of the difference in NPS and the z-statistic.
- Calculate the two-sided p-value and a 95% confidence interval for the NPS change.
- Conclude whether the observed increase is statistically meaningful.
Assumptions
- Survey responses are independent within and across periods.
- Sampling is representative of the same customer population before and after the redesign.
- Sample sizes are large enough for a normal approximation.
- No major concurrent product or pricing changes affected survey sentiment during the measurement window.
