Consumers turned to their mobile devices in growing numbers

Consumers turned to their mobile devices in growing numbers and increasing frequency throughout a given year. Text messaging led as the top mobile activity, with 64% of American mobile subscribers texting that year. A polling firm contacts an SRS of 1300 people chosen from the population of American mobile subscribers. Give the 95% confidence interval for the true proportion of mobile users who text? (Round your answers to three decimal places.)

answer:

......... to ............

Solution

p = 0.64

Here, n = 1300

Z(alpha/2) = Z(0.05/2) = 1.96

95% Confidence Interval

= ( p - Z(alpha/2)*sqrt(p*(1-p)/n) , p + Z(alpha/2)*sqrt(p*(1-p)/n) )

= ( 0.64 - 1.96*sqrt(0.64*(1-0.64)/1300) , 0.64 - 1.96*sqrt(0.64*(1-0.64)/1300) )

= ( 0.614, 0.666)