Business Context
RetailBox, an online marketplace, wants to know whether a new on-site promotion changes average order value. A product analyst sampled completed orders from users who saw the old promotion and users who saw the new promotion.
Problem Statement
Use an appropriate statistical method to determine whether the new promotion changed mean order value. Assume the two samples are independent and large enough for normal approximation.
Given Data
| Group | Sample Size | Mean Order Value | Sample Standard Deviation |
|---|
| Control (old promotion) | 120 | $52.40 | $14.80 |
| Treatment (new promotion) | 135 | $56.10 | $16.20 |
Use a two-sided test with significance level 0.05.
Requirements
- State the null and alternative hypotheses.
- Identify the statistical method you would use and why it is appropriate.
- Calculate the standard error for the difference in sample means.
- Compute the test statistic and approximate p-value.
- Construct a 95% confidence interval for the difference in means.
- State whether the result is statistically significant.
- Give a business recommendation based on both statistical and practical significance.
Assumptions
- Orders are independently sampled across groups.
- The two groups were assigned without systematic bias.
- Sample sizes are large enough that the sampling distribution of the mean difference is approximately normal.
- Variances may differ slightly, so use Welch's two-sample t-test.
