1. **State the problem:** We want to test if there is enough evidence to reject the claim that the average home price in Beaver County is $60,000 at significance level $\alpha = 0.05$. 2. **Set hypotheses:** - Null hypothesis $H_0$: $\mu = 60000$ - Alternative hypothesis $H_a$: $\mu \neq 60000$ (two-tailed test) 3. **Calculate sample mean $\bar{x}$:** Sum all prices and divide by 36. 4. **Calculate sample standard deviation $s$:** Use formula $s = \sqrt{\frac{1}{n-1} \sum (x_i - \bar{x})^2}$. 5. **Calculate test statistic $t$:** $$t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$$ where $\mu_0 = 60000$, $n=36$. 6. **Find critical value:** Degrees of freedom $df = n-1 = 35$. At $\alpha=0.05$ two-tailed, critical $t_{0.025,35} \approx 2.030$. 7. **Decision rule:** If $|t| > 2.030$, reject $H_0$; otherwise, do not reject. 8. **Calculate sample mean:** Sum prices = 2,022,490 $$\bar{x} = \frac{2022490}{36} \approx 56180.28$$ 9. **Calculate sample standard deviation:** Calculate squared deviations, sum = 4,066,927,000 $$s = \sqrt{\frac{4066927000}{35}} \approx 10778.45$$ 10. **Calculate test statistic:** $$t = \frac{56180.28 - 60000}{10778.45/\sqrt{36}} = \frac{-3819.72}{1796.41} \approx -2.13$$ 11. **Compare with critical value:** $|t| = 2.13 > 2.030$, so reject $H_0$. 12. **Conclusion:** There is sufficient evidence at the 0.05 level to reject the agent's claim that the average home price is $60,000$.