Question

x) 14.51 In a simple random sample of 1500 young people, 86% had earned a high school diploma. Complete parts a through d below. a. What is the standard error for this estimate of the percentage of all young people who eamed a high school diploma? Question Help (Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer 3 parts remaining Clear All

Answer 1

Solution

Given that,

p = 86% = 0.86

1 - p = 1 - 0.86 = 0.14

n = 1500

The standard error of the sampling distribution is ,  

$\sigma$_{$\hat p$} =  $\sqrt$p ( 1 - p ) / n

$\sigma$_{$\hat p$} =  $\sqrt$ (0.86 * 0.14) / 1500 = 0.0090

$\sigma$_{$\hat p$} = 0.0090