Business Context
StreamCart, a grocery delivery app, noticed that weeks with higher paid marketing spend also had higher order volume. The growth team wants to know whether this relationship proves that increasing ad spend causes more orders.
Problem Statement
You are given 8 weeks of data on marketing spend and total orders. Quantify the linear relationship using correlation, test whether it is statistically different from zero, and explain why a strong correlation does not by itself establish causation.
Given Data
| Week | Marketing Spend ($000) | Orders (000) |
|---|
| 1 | 20 | 100 |
| 2 | 22 | 104 |
| 3 | 25 | 108 |
| 4 | 28 | 115 |
| 5 | 30 | 120 |
| 6 | 35 | 130 |
| 7 | 40 | 145 |
| 8 | 45 | 150 |
Assume a significance level of 0.05 for testing whether the population correlation is zero.
Requirements
- Calculate the sample Pearson correlation between marketing spend and orders.
- Test the null hypothesis that the population correlation is zero.
- Compute the corresponding t-statistic and p-value.
- State whether the correlation is statistically significant at α=0.05.
- Explain clearly, in business terms, why correlation does not imply causation.
- Give at least two plausible confounders or alternative explanations for the observed relationship.
Assumptions
- Treat each week as an independent observation.
- Use Pearson correlation for a linear relationship.
- Assume the test statistic follows a t-distribution with n−2 degrees of freedom under the null.
