Answer
We are 99% confident that the population proportion of Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage falls between 0.430 and 0.510.
Work Step by Step
$x$ = 493, n = 1050, $\hat{p}$ = 0.470, 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 = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 2.5758\cdot \sqrt{\frac{0.470(0.53)}{1050}}$ $\approx$ 0.03967
iv) Find lower bound of CI:
$\hat{p}$ - E
= 0.470 - 0.03967
= 0.43033
$\approx$ 0.430
v) Find upper bound of CI:
$\hat{p}$ + E
= 0.470 + 0.03967
= 0.50967
$\approx$ 0.510
