1. **State the problem:** We want to test the claim that the mean braking distance for SUVs with compound 1 tires ($\mu_1$) is less than that for compound 2 tires ($\mu_2$). 2. **Given data:** - Mean for compound 1: $\bar{x}_1 = 74$ - Standard deviation for compound 1: $\sigma_1 = 13.4$ - Mean for compound 2: $\bar{x}_2 = 77$ - Standard deviation for compound 2: $\sigma_2 = 14.3$ - Sample size for each: $n_1 = n_2 = 41$ - Significance level: $\alpha = 0.05$ 3. **Hypotheses:** - Null hypothesis: $H_0: \mu_1 = \mu_2$ - Alternative hypothesis: $H_a: \mu_1 < \mu_2$ 4. **Formula for the test statistic (z-test for difference of means with known population standard deviations):** $$ z = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} $$ 5. **Calculate the standard error:** $$ SE = \sqrt{\frac{13.4^2}{41} + \frac{14.3^2}{41}} = \sqrt{\frac{179.56}{41} + \frac{204.49}{41}} = \sqrt{4.379 + 4.987} = \sqrt{9.366} \approx 3.06 $$ 6. **Calculate the test statistic:** $$ z = \frac{74 - 77}{3.06} = \frac{-3}{3.06} \approx -0.98 $$ **Final answer:** The value of the test statistic is approximately $-0.98$.