Answer to Question #189806 in Statistics and Probability for Jenny Rose Domecil

Question

x=500,n=812,95% confidence

Answer 1

$\hat p=\frac{x}{n}=\frac{500}{812}=0.6158.$

$95\%CI=(\hat p-1.96\sqrt{\frac{\hat p(1-\hat p)}{n}}, \hat p+1.96\sqrt{\frac{\hat p(1-\hat p)}{n}})=$

$=(0.6158-1.96\sqrt{\frac{0.6158(1-0.6158)}{812}}, 0.6158+1.96\sqrt{\frac{0.6158(1-0.6158)}{812}})=$

$=(0.5823,0.6492).$