## Elementary Statistics (12th Edition)

a) The best point estimate is equal to the proportion of the sample (x) divided by the sample size: $\hat{p}=\frac{x}{n}=\frac{1083}{2518}=0.43.$ b)$E=z_{\frac{\alpha}{2}}\cdot \sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}=1.645\cdot \sqrt{\frac{0.43\cdot (1-0.43)}{2518}}=0.0162.$ c) Confidence interval: E is between $\hat{p}-E$ and $\hat{p}+E$, hence p is between 0.43-0.0162=0.4138 and 0.43+0.0162=0.4462. d)We are 90% sure that p is between 0.4138 and 0.4462.