Answer
Lower Bound: 0.566; Upper Bound: 0.634
Work Step by Step
$x$ = 540, n = 900, 96% confidence
i) $\hat{p}$ = $\frac{x}{n}$ = $\frac{540}{900}$ = 0.6
ii) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.96$ = 0.04
$\frac{0.04}{2}$ = 0.02
iii) The z-score that corresponds to 0.02 is 2.0537
iv) Find margin of error
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 2.0537 \cdot \sqrt{\frac{0.600(0.400)}{900}}$ $\approx$ 0.034
v) Find lower bound of CI:
$\hat{p}$ - E = 0.6 - 0.034 = 0.566
vi) Find upper bound of CI:
$\hat{p}$ + E = 0.6 + 0.034 = 0.634
