Answer
Lower Bound: 0.140; Upper Bound: 0.160
Work Step by Step
$x$ = 542, n = 3611, $\hat{p}$ = 0.150, 90% confidence
i) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.90$ = 0.10
$\frac{0.10}{2}$ = 0.05
ii) The z-score that corresponds to 0.05 is 1.645
iii) Find margin of error:
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 1.645 \cdot \sqrt{\frac{0.150(0.850)}{3611}}$ $\approx$ 0.00977
iv) Find lower bound of CI:
$\hat{p}$ - E
= 0.150 - 0.00977
= 0.14023
$\approx$ 0.140
v) Find upper bound of CI:
$\hat{p}$ + E
= 0.150 + 0.00977
= 0.15977
$\approx$ 0.160
