1. **State the problem:** We want to test the claim that the population mean $\mu$ is different from 9 using a hypothesis test at the 0.05 significance level. 2. **Write the hypotheses:** - Null hypothesis: $H_0: \mu = 9$ - Alternative hypothesis: $H_1: \mu \neq 9$ 3. **Determine the type of test:** Since $H_1$ uses $\neq$, this is a two-tailed test. 4. **Test statistic:** Given as $2.024$ (rounded to 3 decimal places). 5. **P-value:** Given as $0.043$ (rounded to 3 decimal places). 6. **Shading the p-value area on the standard normal distribution:** - Because this is a two-tailed test, shade the areas in both tails of the normal curve. - Each tail corresponds to half of the p-value, so shade the left tail area of $0.0215$ and the right tail area of $0.0215$. - The shaded regions represent the probability of observing a test statistic as extreme or more extreme than $\pm 2.024$ under the null hypothesis. 7. **Decision rule:** - Since the p-value $0.043$ is less than the significance level $0.05$, we reject the null hypothesis. 8. **Conclusion:** There is sufficient evidence at the 0.05 level to conclude that the population mean is different from 9. This shading visually represents the rejection regions in both tails of the standard normal distribution corresponding to the p-value.