Question

In a survey on downloading music, a poll asked 724 internet users if they "ever downloaded music from an internet site that was not authorized by a recording company, or not" and 16% responded "yes". Construct a 99% confidence interval for the true proportion of internet users who have downloaded music from an internet site that was not authorized.

What is the confidence interval?

Answer 1

Solution:
Given in the question
Number of sample = 724
Sample proportion (p^) or point estimate = 0.16 or 16% responding yes
We need to construct 99% confidence interval for the true proportion of internet users who have downloaded music from an internet site that was not authorized which can be calculated as
p^ +/- Zalpha/2 sqrt(p^*(1-p^)/n)
Here confidence level = 0.99
alpha = 0.01, alpha/2 = 0.005
From Z table we found Zalpha/2 = 2.5758
so 99% confidence interval is
0.16 +/- 2.5758*sqrt(0.16*(1-0.16)/724)
0.16 +/- 2.5758*0.013625
0.16+/- 0.035
So 99% confidence interval is 0.125 to 0.195
So we are 99% confident that the true proportion of internet users who have downloaded music from an internet site that was not authorized is between 0.125 to 01.95