Question

Construct a confidence interval for the population proportion p.

Sample size, n=256, success number, x=130, 90% confidence.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 130 / 256 = 0.508

1 - $\hat p$ = 1 - 0.508 = 0.492

Z_$\alpha$/2 = 1.645

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

= 1.645 * ($\sqrt$((0.508 * 0.492) / 256)

Margin of error = E = 0.051

A 90% confidence interval for population proportion p is ,

$\hat p$ - E < p < $\hat p$ + E

0.508 - 0.051 < p < 0.508 + 0.051

0.457 < p < 0.559

The 90% confidence interval for the population proportion p is : 0.457 , 0.559