Answer
Lower Bound: 0.520; Upper Bound: 0.560.
We are 90% Confident that the population proportion of adult Americans, without tattoos, who believe individuals with tattoos are more rebellious falls between 0.520 and 0.560
Work Step by Step
$x$ = 944, n = 1748, $\hat{p}$ = 0.540, 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 = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 1.645\cdot \sqrt{\frac{0.540(0.46)}{1748}}$ $\approx$ 0.01961
iv) Find lower bound of CI:
$\hat{p}$ - E
= 0.540 - 0.01961
= 0.52039
$\approx$ 0.520
v) Find upper bound of CI:
$\hat{p}$ + E
= 0.540 + 0.01961
= 0.55961
$\approx$ 0.560
