Question

Construct a 90% confidence interval of the population proportion using the given information x = 180, n=300 Click here to view the table of critical values. The lower bound is The upper bound is (Round to three decimal places as needed.) Enter your answer in each of the answer boxes

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 180 / 300 = 0.60

1 - $\hat p$ = 1 - 0.60 = 0.40

Z $\alpha$ /2 = Z_0.05 = 1.645

Margin of error = E = Z _{$\alpha$ / 2} * (( $\hat p$ * (1 - $\hat p$ )) $\sqrt$ / n)

= 1.645 ( $\sqrt$ ((0.60 * 0.40) / 300)

= 0.047

A 90% confidence interval for population proportion p is ,

$\hat p$ ± E

= 0.60  ± 0.047

= ( 0.553, 0.647 )

lower bound = 0.553

upper bound = 0.647