1. **State the problem:** We want to test if the mean slab thickness in Colorado differs from the national average of 67 cm at 99% confidence. 2. **Given data:** Sample thicknesses: 59, 51, 76, 38, 65, 54, 49, 62, 68, 55, 64, 67, 63, 74, 65, 79. 3. **Calculate sample mean $\bar{x}$:** $$\bar{x} = \frac{59 + 51 + 76 + 38 + 65 + 54 + 49 + 62 + 68 + 55 + 64 + 67 + 63 + 74 + 65 + 79}{16} = \frac{1048}{16} = 65.5$$ 4. **Calculate sample standard deviation $s$:** First, find squared deviations: $$\sum (x_i - \bar{x})^2 = (59-65.5)^2 + (51-65.5)^2 + \cdots + (79-65.5)^2 = 1410$$ Then, $$s = \sqrt{\frac{1410}{16-1}} = \sqrt{94} \approx 9.70$$ 5. **Set hypotheses:** - Null hypothesis $H_0$: $\mu = 67$ - Alternative hypothesis $H_a$: $\mu \neq 67$ 6. **Calculate test statistic $t$:** $$t = \frac{\bar{x} - \mu}{s/\sqrt{n}} = \frac{65.5 - 67}{9.70/\sqrt{16}} = \frac{-1.5}{9.70/4} = \frac{-1.5}{2.425} \approx -0.62$$ 7. **Interpretation:** The test statistic is approximately $-0.62$. **Final answer:** $t = -0.62$