Answer
Lower Bound of CI: 0.146; Upper Bound of CI: 0.254
Work Step by Step
$x$ = 30, n = 150, 90% confidence
i) $\hat{p}$ = $\frac{x}{n}$ = $\frac{30}{150}$ = 0.2
ii) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.90$ = 0.10
$\frac{0.10}{2}$ = 0.05
iii) The z-score that corresponds to 0.05 is 1.645
iv) Find margin of error
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 1.645 \cdot \sqrt{\frac{0.2(0.8)}{150}}$ $\approx$ 0.0537
iv) Find lower bound of CI:
$\hat{p}$ - E = 0.2 - 0.0537 = 0.146
v) Find upper bound of CI:
$\hat{p}$ + E = 0.2 + 0.0537 = 0.254
