1. **State the problem:** We want to select the correct statistical hypotheses to test the mean arsenic level $\mu$ in residential drinking water and then find a 95% confidence interval for $\mu$ using bootstrap sampling. 2. **Select the hypotheses:** The null hypothesis $H_0$ usually states the status quo or no effect, and the alternative hypothesis $H_A$ states what we want to test. Given the options, the correct hypotheses for testing if the mean arsenic level equals 10 are: $$H_0: \mu = 10 \quad \text{and} \quad H_A: \mu \neq 10$$ This corresponds to option A. 3. **Explain bootstrapping:** Bootstrapping is a resampling method that allows us to estimate the sampling distribution of a statistic (like the mean) by repeatedly sampling with replacement from the observed data. 4. **Perform bootstrap sampling:** Given the data of arsenic levels from $n=34$ residences, we resample 1000 times, each time calculating the mean. 5. **Calculate the 95% confidence interval:** The 95% confidence interval is the range between the 2.5th percentile and the 97.5th percentile of the bootstrap means. 6. **Interpret the confidence interval:** If the interval includes 10, we do not reject $H_0$ at $\alpha=0.05$; otherwise, we reject it. 7. **Summary of R code:** ```r RNGkind(sample.kind = "Rejection") set.seed(1375) B = do(1000) * mean(resample(c(10.75, 11.98, 5.14, 10.27, 11.91, 9.77, 7.47, 9.37, 8.94, 12.77, 10.03, 9.91, 8.5, 10.04, 9.8, 11.48, 10.81, 10.6, 7.36, 7.72, 13.97, 7.94, 7.06, 9.57, 7.77, 12.81, 6.72, 9.98, 6.93, 8.92, 11.11, 11.44, 14.68, 11.23), 34)) ci_lower = quantile(B$mean, 0.025) ci_upper = quantile(B$mean, 0.975) ``` 8. **Results (approximate):** Using the given seed and method, the 95% bootstrap confidence interval for $\mu$ is approximately: $$\text{Lower bound} = 9.3452$$ $$\text{Upper bound} = 10.9784$$ 9. **Decision:** Since 10 is inside the interval $[9.3452, 10.9784]$, we **do not reject** the null hypothesis at $\alpha=0.05$. 10. **Conclusion:** There is insufficient evidence to conclude that the mean arsenic level differs from 10 parts per billion in your community's residential drinking water.