Business Context
SupportHub, a SaaS customer support platform, introduced a new agent-assist feature and wants to know whether it reduces average ticket handle time. A random sample of tickets was collected before and after the rollout.
Problem Statement
Determine whether the new feature reduced mean handle time, and quantify the likely size of the reduction.
Given Data
| Group | Sample Size | Mean Handle Time (minutes) | Sample Standard Deviation (minutes) |
|---|
| Before rollout | 64 | 18.4 | 4.8 |
| After rollout | 49 | 16.9 | 4.2 |
Use a one-tailed two-sample t-test at a significance level of 0.05. Assume independent samples and approximately normal sampling distributions.
Requirements
- State the null and alternative hypotheses.
- Compute the standard error for the difference in means.
- Calculate the t-statistic.
- Estimate the degrees of freedom using Welch's t-test.
- Find the one-tailed p-value and make a decision at α=0.05.
- Construct a 95% confidence interval for the mean difference (μbefore−μafter).
- Interpret whether the result is both statistically and practically meaningful for the business.
Assumptions
- Tickets in the two samples are independent.
- The rollout did not change ticket mix in a way that would heavily bias handle time.
- Sample sizes are large enough for the t-test to be reasonably robust.
- Population variances are not assumed equal, so use Welch's t-test.
