Answer
Lower Bound: 0.306; Upper Bound: 0.360
Work Step by Step
$x$ = 400, n = 1200, 95% confidence
i) $\hat{p}$ = $\frac{x}{n}$ = $\frac{400}{1200}$ = 0.333
ii) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.95$ = 0.05
$\frac{0.05}{2}$ = 0.025
iii) The z-score that corresponds to 0.025 is 1.96
iv) Find the margin of error
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 1.96 \cdot \sqrt{\frac{0.333(0.667)}{1200}}$ $\approx$ 0.027
v) Find lower bound of CI:
$\hat{p}$ - E = 0.333 - 0.027 = 0.306
vi) Find upper bound of CI:
$\hat{p}$ + E = 0.333 + 0.027 = 0.360
