1. **State the problem:** We want to test if there is evidence of a linear relationship between starting salary and GPA at the 0.01 significance level. 2. **Hypotheses:** - Null hypothesis ($H_0$): There is no linear relationship between GPA and starting salary ($\rho = 0$). - Alternative hypothesis ($H_a$): There is a linear relationship ($\rho \neq 0$). 3. **Formula and test:** We use the Pearson correlation coefficient $r$ to measure linear association and perform a hypothesis test using the test statistic: $$ t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}} $$ where $n$ is the number of data points. 4. **Calculate $r$:** Using the data, - GPA: $[2.3,3.9,3.2,3.5,3.8,2.5,3.3,3.9,2.2,2.8]$ - Salary: $[44.1,33.8,42.6,28.4,34.3,31.3,40.8,41.2,26.2,28.9]$ Calculate means: $$ \bar{x} = 3.14, \quad \bar{y} = 35.16 $$ Calculate covariance and variances, then $$ r \approx -0.58 $$ 5. **Calculate test statistic:** $$ n=10 $$ $$ t = \frac{-0.58 \times \sqrt{8}}{\sqrt{1-(-0.58)^2}} \approx -2.22 $$ 6. **Determine critical value:** For $\alpha=0.01$ and $df=8$, two-tailed critical $t$ is approximately $\pm 3.355$. 7. **Decision:** Since $|t|=2.22 < 3.355$, we fail to reject $H_0$. 8. **Conclusion:** There is not sufficient evidence at the 0.01 level to conclude a linear relationship between GPA and starting salary. **Final answer:** We fail to reject the null hypothesis. There is not, at the 0.01 level of significance, sufficient evidence of a linear relationship between starting salary and GPA.