Given: n = 1019
x = 672
[tex]\hat{p}=\frac{672}{1019}=0.66[/tex]z-score for 95% confidence interval, Z = 1.96
a) Margin of Error, MoE
[tex]\begin{gathered} MoE=Z\sqrt[]{\frac{\hat{p}(1-\hat{p})}{n}}=1.96\cdot\sqrt[]{\frac{0.66(1-0.66)}{1019}}=.0291 \\ \\ \end{gathered}[/tex]b) 95% confidence interval estimate of the proportion, E
[tex]\begin{gathered} E=\hat{p}\pm Z\sqrt[]{\frac{\hat{p}(1-\hat{p})}{n}}=0.66\pm1.96\cdot\sqrt[]{\frac{0.66(1-0.66)}{1019}}=0.66\pm0.0291 \\ 0.66+0.0291=0.6891 \\ 0.66-0.0291=0.6309 \\ (0.6891,0.6309) \end{gathered}[/tex]Answer:
a) MoE = 0.0291 = 2.91%
b) The 95% confidence interval is (0.6891, 0.6309)
