Business Context
StreamCart changed its post-purchase support workflow and wants to know whether customer satisfaction improved. Survey responses are on a 1-5 scale, and the analytics team collected independent random samples before and after the change.
Problem Statement
Determine whether the change in mean consumer satisfaction score is statistically significant using a two-sample hypothesis test.
Given Data
| Group | Sample Size | Mean Satisfaction Score | Standard Deviation |
|---|
| Before change | 180 | 4.02 | 0.62 |
| After change | 165 | 4.16 | 0.58 |
Use a two-sided test with significance level 0.05.
Requirements
- State the null and alternative hypotheses.
- Compute the standard error for the difference in sample means.
- Calculate the test statistic for the change in mean satisfaction.
- Approximate the p-value and decide whether the result is statistically significant at α=0.05.
- Construct a 95% confidence interval for the mean difference.
- Interpret the result in business terms: does the workflow change appear to improve satisfaction, and is the effect practically meaningful?
Assumptions
- The before and after samples are independent.
- Satisfaction scores are approximately normally distributed in each group, or the sample sizes are large enough for the Central Limit Theorem to apply.
- The survey sampling process did not systematically change between periods.
- Treat the 1-5 satisfaction score as an approximately interval-scale metric for mean comparison.
