Here’s a breakdown of the problem based on the uploaded image:

Summary:

1. Correlation Coefficient (r):

   • Computed as 0.83, rounded to 2 decimal places. This indicates a strong positive correlation.

2. Hypotheses:

   • Null Hypothesis: $H_0: \rho = 0$ (no correlation).
   • Alternative Hypothesis: $H_1: \rho \neq 0$ (there is a correlation).
   • The p-value: 0.0223, rounded to 4 decimal places.

3. Hypothesis Test Conclusion:

   • With a significance level ($\alpha = 0.05$), the p-value ($0.0223 < 0.05$) leads to rejecting the null hypothesis.
   • The conclusion: "There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful."

4. Coefficient of Determination (r²):

   • $r^2$ quantifies the proportion of variance in Money explained by Time. Using $r = 0.83$:
     $r^2 = 0.83^2 = 0.6889$ Rounded to two decimal places: 0.69.

Would you like detailed explanations for any specific part of this solution?

Follow-up Questions:

1. How is the correlation coefficient (r) calculated from the data?
2. What does the p-value represent in this context?
3. How does the hypothesis test help validate the relationship?
4. What does the coefficient of determination (r²) imply about the relationship?
5. Why is it important to set the significance level ($\alpha$) before conducting the test?

Tip:

The correlation coefficient only measures linear relationships. Always check if the relationship might be non-linear before interpreting results.