Answer:
Given:
The sample proportion $ (\hat{p}) = 0.67 $
The sample size $ (n) = 90 $
The confidence interval level $ = 95\% $
Solution:
The significance level $ (\alpha) : $
$ \alpha = 1 – 0.95 $
$ = 0.05 $
The critical value $ (z_c) : $
$ z_c = z_{\alpha/2} $
$ = z_{0.05/2} $
$ = 1.96 $
The confidence interval:
$CI = \hat{p} \pm z_c \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $
$ = 0.67 \pm 1.96 \times \sqrt{\frac{0.67(1-0.67)}{90}} $
$ = (0.573 < p < 0.767) $
Final Answer:
The 95% confidence interval $= (0.573 < p < 0.767) $
