Answer
Lower Bound: 0.319; Upper Bound: 0.481
Work Step by Step
$x$ = 80, n = 200, 98% confidence
i) $\hat{p}$ = $\frac{x}{n}$ = $\frac{80}{200}$ = 0.400
ii) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.98$ = 0.02
$\frac{0.02}{2}$ = 0.01
iii) The z-score that corresponds to 0.01 is 2.3263
iv) Find margin of error
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 2.3263 \cdot \sqrt{\frac{0.400(0.600)}{200}}$ $\approx$ 0.081
iv) Find lower bound of CI:
$\hat{p}$ - E = 0.400 - 0.081 = 0.319
v) Find upper bound of CI:
$\hat{p}$ + E = 0.400 + 0.081 = 0.481
