Question

In a survey on downloading​ music, a poll asked 705 Internet users if they​ "ever downloaded music from an Internet site that was not authorized by a record​ company, or​ not," and 18​% responded​ "yes." Construct a 90​% 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? Select the correct choice below​ and, if​ necessary, fill in the answer boxes within your choice.

A. The 90​% confidence interval is ( ________% ________%)

​(Round to one decimal place as​ needed.)

B. The conditions for constructing a confidence interval are not satisfied.

Answer 1

Answer)

Given P = 0.18

N = 705

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 126.9

N*(1-p) = 578.1

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z for 90% confidence level from z table is 1.645

Margin of error (MOE) = Z*√P*(1-P)/√N

= 1.645*√0.18*(1-0.18)/√705

= 0.02380205873

Confidence interval is given by

(P-MOE, P+MOE)

(0.15619794126, 0.20380205873)

(15.6%, 20.4%)