1. **Problem Statement:** Analyze if customer groups defined by age and income differ significantly in satisfaction and total spending using MANOVA. 2. **Formula and Concepts:** MANOVA tests differences in multiple dependent variables across groups. Key statistic: Wilks' Lambda $$\Lambda = \frac{\det(E)}{\det(E+H)}$$ where $E$ is error sum of squares and $H$ is hypothesis sum of squares. Smaller $\Lambda$ indicates group differences. 3. **Data Preparation:** Group customers by age and income into categories (e.g., low, medium, high). Dependent variables: satisfaction score and total spending. 4. **Assumptions:** - Multivariate normality of dependent variables within groups. - Homogeneity of covariance matrices (checked by Box's M test). - Independence of observations. 5. **Perform MANOVA:** Model: $$\text{Dependent} = \text{Age Group} + \text{Income Group} + \text{Age Group} \times \text{Income Group}$$ Calculate Wilks' Lambda and associated F-statistic. 6. **Interpretation:** If Wilks' Lambda is significant (p-value < 0.05), conclude that satisfaction and spending differ by age and/or income groups. 7. **Hypothesis Testing for Each Dependent Variable:** Conduct follow-up ANOVAs for satisfaction and spending separately to identify which variable(s) differ. **Final Answer:** Using MANOVA with age and income groups as factors and satisfaction and total spending as dependent variables, we test for significant differences. A significant Wilks' Lambda indicates that customer satisfaction and spending vary across demographic groups, guiding targeted marketing strategies.