Business Context
BrightCart, an e-commerce retailer, is reviewing last month’s paid search campaign. Finance wants to know whether the observed variances are favorable or unfavorable, but the answer depends on the metric: lower cost is usually favorable, while lower output is usually unfavorable.
Problem Statement
You are given the campaign’s planned and actual results. Determine the direction of each variance in context and assess whether the shortfall in conversions is statistically meaningful relative to normal month-to-month variability.
Given Data
| Metric | Planned | Actual |
|---|
| Ad spend | $120,000 | $114,000 |
| Conversions | 4,000 | 3,850 |
| Revenue per conversion | $42.50 | $42.50 |
| Historical monthly conversion standard deviation | 90 | 90 |
| Significance level | 0.05 | 0.05 |
Assume the historical standard deviation of monthly conversions is stable and approximately normal, based on prior months.
Requirements
- Compute the spend variance in dollars and classify it as favorable or unfavorable.
- Compute the conversion variance in units and classify it as favorable or unfavorable.
- Compute the revenue impact of the conversion variance.
- Test whether the conversion shortfall is statistically significant using a z-score.
- Explain why the same sign of variance can be favorable for one metric and unfavorable for another.
- Give a business recommendation based on both the accounting variance and the statistical result.
Assumptions
- Lower ad spend than budget is favorable if performance is unchanged.
- Lower conversions than plan are unfavorable because conversions are the primary output metric.
- Monthly conversions are approximately normally distributed around plan with known standard deviation of 90.
- Use a two-sided 5% significance threshold to judge whether actual conversions differ materially from plan.
