Question

2 Iha Gallup poll of 557 randomly selected adults, 284 said that they were underpaid. a struct a 95% confidence interval estimate the percentage of all adults who say that hey are underpaid. (20 points)

Answer 1

Q.2) Given that, n = 557 and x = 284

sample proportion $(\hat p)$ = 284 / 557 = 0.5099

A 95% confidence level has significance level of 0.05 and critical value is, $Z_{\alpha/2} = 1.96$

The 95% confidence interval for p is,

$\hat p \pm Z_{\alpha/2} * \sqrt {\frac {\hat p *(1-\hat p)}{n}}$

$0.5099 \pm 1.96 * \sqrt {\frac {0.5099 *(1-0.5099)}{557}}$

$0.5099 \pm 0.0415$

$0.5099 - 0.0415 < p < 0.5099 &plus; 0.0415$

$0.4684 < p < 0.5514$

Therefore, the 95% confidence interval estimate the percentage of all adults who say that they are underpaid is,

( 0.4684, 0.5514 )