Answer
We are 99% confident that the population proportion of Americans, 18 or older, for which the issue of family values is extremely or very important in determining their vote for president falls between 0.715 and 0.785.
Work Step by Step
$x$ = 768, n = 1024, $\hat{p}$ = 0.75, 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 = $z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = 2.5758\cdot \sqrt{\frac{0.75(0.25)}{1024}}$ $\approx$ 0.03485
iv) Find lower bound of CI:
$\hat{p}$ - E
= 0.75 - 0.03485
= 0.71515
$\approx$ 0.715
v) Find upper bound of CI:
$\hat{p}$ + E
= 0.75 + 0.03485
= 0.78485
$\approx$ 0.785
