In a survey of 2,483 website​ users...

Question

In a survey of 2,483 website​ users, 1,930 cited​ "seeing photos or​ videos" as a major reason why they use a​ website, while 1,217 cited​ "keeping up with news and current​ events" as a major reason why they use a website. Complete parts​ (a) through​ (c) below.

a. Construct a​ 95% confidence interval estimate for the population proportion of website users who cited​ "seeing photos or​ videos" as a major reason why they use a website.

____ ≤ π ≤ ____ (Round to four decimal places as​ needed.)

b. Construct a​ 95% confidence interval estimate for the population proportion of website users who cited​ "keeping up with news and current​ events" as a major reason why they use a website.

____ ≤ π ≤ ____ (Round to four decimal places as​ needed.)

Answer 1

n = 2483

z-critical for 95% CI is 1.96

a)

phat = 1930/2483 = 0.7773

CI = phat +/- z-critical * sqrt(phat * (1-phat)/n) = 0.7773 +/- 1.96 * sqrt(0.7773*0.2227/2483) = (0.7609,0.7947)

b)

phat = 1217/2483 = 0.4901

CI = phat +/- z-critical * sqrt(phat * (1-phat)/n) = 0.4901 +/- 1.96 * sqrt(0.4901*0.5099/2483) = (0.4704,0.5098)