Answer
Lower Bound: 0.401; Upper Bound: 0.459
Work Step by Step
$x$ = 496, n = 1153, $\hat{p}$ = 0.430, 95% confidence
i) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.95$ = 0.05
$\frac{0.05}{2}$ = 0.025
ii) The z-score that corresponds to 0.025 is 1.96
iii) Find margin of error:
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 1.96\cdot \sqrt{\frac{0.430(0.57)}{1153}}$ $\approx$ 0.028577
iv) Find lower bound of CI:
$\hat{p}$ - E
= 0.430 - 0.028577
= 0.401423
$\approx$ 0.401
v) Find upper bound of CI:
$\hat{p}$ + E
= 0.430 + 0.028577
= 0.458577
$\approx$ 0.459
