1. **State the problem:** We want to test if the fuel economy of E10 fuel is the same as regular unleaded fuel using a paired t-test at a 5% significance level. 2. **Data given:** E10: $9.6, 11.2, 9.2, 14.1, 11.5, 9.2, 11.8, 12.3, 12.0, 10.3$ Regular unleaded: $10.7, 11.8, 9.3, 13.4, 12.4, 9.5, 12.2, 13.1, 12.8, 11.0$ 3. **Hypotheses:** - Null hypothesis $H_0$: The mean difference $\mu_d = 0$ (no difference in fuel economy). - Alternative hypothesis $H_a$: The mean difference $\mu_d \neq 0$ (there is a difference). 4. **Formula for paired t-test:** $$ t = \frac{\bar{d} - \mu_0}{s_d / \sqrt{n}} $$ where $\bar{d}$ is the mean of differences, $s_d$ is the standard deviation of differences, $n$ is the number of pairs, and $\mu_0=0$ under $H_0$. 5. **Calculate differences (E10 - Regular):** $$ d = [-1.1, -0.6, -0.1, 0.7, -0.9, -0.3, -0.4, -0.8, -0.8, -0.7] $$ 6. **Calculate mean difference $\bar{d}$:** $$ \bar{d} = \frac{-1.1 -0.6 -0.1 +0.7 -0.9 -0.3 -0.4 -0.8 -0.8 -0.7}{10} = \frac{-5.0}{10} = -0.5 $$ 7. **Calculate standard deviation $s_d$ of differences:** First find squared deviations from mean: $$ (d_i - \bar{d})^2 = [(-1.1 + 0.5)^2, (-0.6 + 0.5)^2, (-0.1 + 0.5)^2, (0.7 + 0.5)^2, (-0.9 + 0.5)^2, (-0.3 + 0.5)^2, (-0.4 + 0.5)^2, (-0.8 + 0.5)^2, (-0.8 + 0.5)^2, (-0.7 + 0.5)^2] $$ $$ = [0.36, 0.01, 0.16, 1.44, 0.16, 0.04, 0.01, 0.09, 0.09, 0.04] $$ Sum = 2.4 $$ s_d = \sqrt{\frac{2.4}{10-1}} = \sqrt{0.2667} \approx 0.5164 $$ 8. **Calculate t-statistic:** $$ t = \frac{-0.5 - 0}{0.5164 / \sqrt{10}} = \frac{-0.5}{0.1632} \approx -3.06 $$ 9. **Degrees of freedom:** $df = n-1 = 9$ 10. **Find critical t-value for two-tailed test at $\alpha=0.05$ and $df=9$:** $$ t_{crit} \approx \pm 2.262 $$ 11. **Decision:** Since $|t| = 3.06 > 2.262$, we reject the null hypothesis. 12. **Conclusion:** There is significant evidence at the 5% level to conclude that the fuel economy of E10 is different from regular unleaded. **Using a GDC:** - Enter the differences into a list. - Use the T-Test function with $\mu_0=0$, paired data. - The GDC will output the t-statistic and p-value confirming the above calculations. Final answer: Reject $H_0$. Fuel economies differ significantly.