1. **Stating the problem:** We have two brands of cars with measurements for 8 cars each. The differences between Brand 1 and Brand 2 for each car are given. We want to test the hypothesis about the mean difference $\mu_d$. 2. **Hypotheses:** - Null hypothesis $H_0$: $\mu_d = 0$ (no difference in means) - Alternative hypothesis $H_1$: $\mu_d \neq 0$ (there is a difference in means) 3. **Data:** Differences $d_i$ are: $0.15, -0.02, 0.14, -0.04, 0.22, -0.11, 0.18, -0.08$ 4. **Calculate the sample mean difference $\bar{d}$:** $$\bar{d} = \frac{1}{8}(0.15 - 0.02 + 0.14 - 0.04 + 0.22 - 0.11 + 0.18 - 0.08) = \frac{0.44}{8} = 0.055$$ 5. **Calculate the sample standard deviation $s_d$:** First, find squared deviations: $$(0.15 - 0.055)^2 = 0.009025$$ $$(-0.02 - 0.055)^2 = 0.005625$$ $$(0.14 - 0.055)^2 = 0.007225$$ $$(-0.04 - 0.055)^2 = 0.009025$$ $$(0.22 - 0.055)^2 = 0.027225$$ $$(-0.11 - 0.055)^2 = 0.027225$$ $$(0.18 - 0.055)^2 = 0.015625$$ $$(-0.08 - 0.055)^2 = 0.018225$$ Sum of squared deviations = $0.1182$ Sample variance: $$s_d^2 = \frac{0.1182}{8-1} = \frac{0.1182}{7} \approx 0.016886$$ Sample standard deviation: $$s_d = \sqrt{0.016886} \approx 0.130$$ 6. **Calculate the test statistic $t$:** $$t = \frac{\bar{d} - 0}{s_d / \sqrt{n}} = \frac{0.055}{0.130 / \sqrt{8}} = \frac{0.055}{0.046} \approx 1.20$$ 7. **Degrees of freedom:** $df = n - 1 = 7$ 8. **Conclusion:** Compare $t$ to critical $t$ value for $df=7$ at chosen significance level (e.g., 0.05). Since $|t|=1.20$ is less than critical $t \approx 2.365$, we fail to reject $H_0$. There is not enough evidence to say the mean difference is different from zero. **Final answer:** The test statistic is approximately $t=1.20$ with $7$ degrees of freedom, and we do not reject the null hypothesis $H_0: \mu_d=0$ at the 5% significance level.