Answer
Lower Bound: 0.509; Upper Bound: 0.571
We are 99% confident that the population proportion of adult Americans without tattoos who believe individuals with tattoos are more rebellious falls between 0.509 and 0.571.
Work Step by Step
$x$ = 944, n = 1748, $\hat{p}$ = 0.540, 99% confidence
i) Find $\frac{\alpha}{2}$
$\alpha = 1 - 0.99$ = 0.01
$\frac{0.01}{2}$ = 0.005
ii) The z-score that corresponds to 0.005 is 2.5758
iii) Find margin of error:
E = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 2.5758\cdot \sqrt{\frac{0.540(0.46)}{1748}}$ $\approx$ 0.03071
iv) Find lower bound of CI:
$\hat{p}$ - E
= 0.540 - 0.03071
= 0.50929
$\approx$ 0.509
v) Find upper bound of CI:
$\hat{p}$ + E
= 0.540 + 0.03071
= 0.57071
$\approx$ 0.571
