Answer
Lower Bound: 0.191; Upper Bound: 0.289
Work Step by Step
$x$ = 120, n = 500, 99% confidence
i) $\hat{p}$ = $\frac{x}{n}$ = $\frac{120}{500}$ = 0.24
ii) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.99$ = 0.01
$\frac{0.01}{2}$ = 0.005
iii) The z-score that corresponds to 0.005 is 2.5758
iv) Find margin of error
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 2.5758 \cdot \sqrt{\frac{0.24(0.76)}{500}}$ $\approx$ 0.049
iv) Find lower bound of CI:
$\hat{p}$ - E = 0.24 - 0.049 = 0.191
v) Find upper bound of CI:
$\hat{p}$ + E = 0.24 + 0.049 = 0.289
