Satisfaction Score Change Significance Test

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

Use a two-sided test with significance level 0.05.

Requirements

1. State the null and alternative hypotheses.
2. Compute the standard error for the difference in sample means.
3. Calculate the test statistic for the change in mean satisfaction.
4. Approximate the p-value and decide whether the result is statistically significant at $\alpha = 0.05$.
5. Construct a 95% confidence interval for the mean difference.
6. 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.