To determine if the relationship between the two variables is statistically significant at the $\alpha = 0.05$ level, we need to compare the absolute value of the Pearson correlation coefficient $|r|$ with the critical value for $n = 9$.

Given:

• Sample size $n = 9$
• Pearson correlation coefficient $r \approx -0.676$
• Critical value for $n = 9$ at $\alpha = 0.05$ is $0.666$

The absolute value of $r$ is $|r| = 0.676$.

Since $0.676$ is greater than the critical value $0.666$ at the $\alpha = 0.05$ level, the correlation coefficient is statistically significant.

Therefore, the relationship between the two variables is statistically significant at the $\alpha = 0.05$ level.

Would you like more details or have any questions?

Here are 5 questions you might ask:

1. How is the Pearson correlation coefficient calculated?
2. What does it mean for a correlation to be statistically significant?
3. Can the Pearson correlation coefficient be used for non-linear relationships?
4. How do different sample sizes affect the critical values of the Pearson correlation coefficient?
5. What are some limitations of using the Pearson correlation coefficient?

Tip: The closer the absolute value of the Pearson correlation coefficient is to 1, the stronger the linear relationship between the variables.