Answer
Lower Bound: 0.488; Upper Bound: 0.550
Work Step by Step
$x$ = 521, n = 1003, $\hat{p}$ = 0.519, 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 = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 1.96\cdot \sqrt{\frac{0.519(0.481)}{1003}}$ $\approx$ 0.03092
iv) Find lower bound of CI:
$\hat{p}$ - E
= 0.519 - 0.03092
= 0.48808
$\approx$ 0.488
v) Find upper bound of CI:
$\hat{p}$ + E
= 0.519 + 0.03092
= 0.54992
$\approx$ 0.550
