Answer
Lower Bound: 0.759; Upper Bound: 0.805
Work Step by Step
$x$ = 860, n = 1100, 94% confidence
i) $\hat{p}$ = $\frac{x}{n}$ = $\frac{860}{1100}$ = 0.782
ii) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.94$ = 0.06
$\frac{0.06}{2}$ = 0.03
iii) The z-score that corresponds to 0.03 is 1.8808
iv) Find margin of error
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 1.8808 \cdot \sqrt{\frac{0.782(0.218)}{1100}}$ $\approx$ 0.023
iv) Find lower bound of CI:
$\hat{p}$ - E = 0.782 - 0.023 = 0.759
v) Find upper bound of CI:
$\hat{p}$ + E = 0.782 + 0.023 = 0.805
