1. **Problem statement:** We want to compute an approximate 95% confidence interval for the percentage of all American adults who would answer yes to the question about doctors being allowed to end a patient's life by painless means if requested. 2. **Given data:** - Sample size $n = 542$ - Sample proportion $\hat{p} = 0.72$ (72%) 3. **Formula for 95% confidence interval for a proportion:** $$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$ where $z^*$ is the critical value for 95% confidence, approximately $1.96$. 4. **Calculate the standard error (SE):** $$SE = \sqrt{\frac{0.72 \times (1 - 0.72)}{542}} = \sqrt{\frac{0.72 \times 0.28}{542}} = \sqrt{\frac{0.2016}{542}} = \sqrt{0.000372} \approx 0.0193$$ 5. **Calculate the margin of error (ME):** $$ME = 1.96 \times 0.0193 \approx 0.0379$$ 6. **Construct the confidence interval:** $$0.72 \pm 0.0379$$ which gives - Lower bound: $0.72 - 0.0379 = 0.6821$ - Upper bound: $0.72 + 0.0379 = 0.7579$ 7. **Interpretation:** We are 95% confident that the true percentage of all American adults who would answer yes is between 68.21% and 75.79%.