## Elementary Statistics (12th Edition)

The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=0.64.$ $\alpha=1-(confidence \ level)=1-0.9=0.1.$ According to the table: $z_{\alpha/2}=z_{0.05}=1.645.$ $E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.645\cdot \sqrt{\frac{0.64\cdot (1-0.64)}{1011}}=0.0248.$ Confidence interval: p is between 0.64-0.0248=0.6152 and 0.64+0.0248=0.6648.