1. **State the problem:** We want to test if there is a significant difference between the average scores of Evaluator 1 and Evaluator 2 for 20 patients. Let $\mu_d = \mu_1 - \mu_2$ be the mean difference. 2. **Determine hypotheses:** The correct hypotheses for testing if the evaluators differ are: $$H_0: \mu_d = 0$$ $$H_a: \mu_d \neq 0$$ This corresponds to option B. 3. **Calculate differences $d_i$:** For each patient, compute $d_i = \text{Evaluator 1} - \text{Evaluator 2}$: Patient differences: $5.1-6.3 = -1.2$, $5.3-6.0 = -0.7$, $5.4-5.7 = -0.3$, $5.5-6.0 = -0.5$, $5.6-6.4 = -0.8$, $5.6-5.9 = -0.3$, $5.9-7.1 = -1.2$, $6.5-6.6 = -0.1$, $7.2-8.6 = -1.4$, $7.8-8.3 = -0.5$, $8.5-8.2 = 0.3$, $8.7-8.3 = 0.4$, $9.1-8.8 = 0.3$, $9.1-8.8 = 0.3$, $9.7-10.3 = -0.6$, $10.1-10.4 = -0.3$, $10.2-10.4 = -0.2$, $10.3-11.2 = -0.9$, $11.2-12.0 = -0.8$, $11.3-11.5 = -0.2$ 4. **Calculate sample mean difference $\bar{d}$:** $$\bar{d} = \frac{\sum d_i}{n} = \frac{-1.2 -0.7 -0.3 -0.5 -0.8 -0.3 -1.2 -0.1 -1.4 -0.5 + 0.3 + 0.4 + 0.3 + 0.3 -0.6 -0.3 -0.2 -0.9 -0.8 -0.2}{20} = \frac{-8.2}{20} = -0.41$$ 5. **Calculate sample standard deviation $s_d$:** First, compute squared deviations: $$\sum (d_i - \bar{d})^2 = 6.658$$ Then, $$s_d = \sqrt{\frac{\sum (d_i - \bar{d})^2}{n-1}} = \sqrt{\frac{6.658}{19}} = \sqrt{0.3504} = 0.592$$ 6. **Calculate test statistic $t$:** $$t = \frac{\bar{d} - 0}{s_d / \sqrt{n}} = \frac{-0.41}{0.592 / \sqrt{20}} = \frac{-0.41}{0.1324} = -3.10$$ 7. **Calculate p-value:** Degrees of freedom $df = n-1 = 19$. Using a two-tailed t-test, $$p\text{-value} = 2 \times P(T \leq -3.10) \approx 2 \times 0.003 = 0.006$$ 8. **State conclusion:** Since $p$-value $=0.006 < 0.05$, we reject $H_0$. **Conclusion:** There is sufficient evidence that the average cardiac outputs measured by the two evaluators differ. Final answers: - Hypotheses: $H_0: \mu_d = 0$, $H_a: \mu_d \neq 0$ - Test statistic: $t = -3.10$ - p-value: $0.006$ - Conclusion: Reject $H_0$. There is sufficient evidence that the average cardiac outputs measured by the two evaluators differ.