Business Context
BrightCart, an online retail platform, launched a personalized email campaign and wants to validate whether the campaign increased average order value (AOV) versus the standard promotional email.
Problem Statement
You are given summary statistics from a randomized experiment. Use appropriate statistical methods to validate whether the observed difference in mean AOV is likely real or due to sampling noise.
Given Data
| Group | Sample Size | Mean AOV | Standard Deviation |
|---|
| Control (standard email) | 160 | $48.20 | $12.50 |
| Treatment (personalized email) | 145 | $51.10 | $13.40 |
Additional test settings:
| Parameter | Value |
|---|
| Significance level | 0.05 |
| Test type | Two-sample, two-tailed |
Requirements
- State the null and alternative hypotheses.
- Choose an appropriate statistical test and explain why it fits this data.
- Calculate the standard error of the difference in means.
- Compute the test statistic and approximate p-value.
- Construct a 95% confidence interval for the mean difference.
- Decide whether the analysis is statistically significant at the 5% level.
- Briefly explain how these methods help validate an analysis in practice.
Assumptions
- Users were randomly assigned to control and treatment.
- Orders are independent across users.
- Sample sizes are large enough for the sampling distribution of the mean difference to be approximately normal.
- Population variances may differ, so do not assume equal variance unless justified.
