In a simple random sample of 1500 young people, 85% had earned a high school dip
ID: 3359200 • Letter: I
Question
In a simple random sample of
1500 young people, 85% 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 earned a high school diploma? 0.0092
(Round to four decimal places as needed.)
b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young people who earned a high school diploma. 1.8%
(Round to one decimal place as needed.)
c. Report the 95% confidence interval for the percentage of all young people who earned a high school diploma.
-------- %, --------%
(Round to one decimal place as needed.)
Explanation / Answer
Given n=1500 and p=0.85
a) Standard error =sqrt((pq)/n)=sqrt((o.85*0.15)/1500) =0.0092
b) Given C=95%
Margin of error =Z* SE(p) =1.96*0.0092=0.018=1.8%
c) 95% CI for P is
P =(p-E, p+E) =(0.85-0.018, 0.85-0.018) =(83.1%,87.8%)