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 62% of American mobile subscribers texting that year. A polling firm contacts an SRS of 1140 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.)

Solution

SRS = 1140 people

sample proportion = 62% = 0.62

Std Error = sqrt[p * (1 - p)/n] = sqrt[0.62 * (1 - 0.62)/1140] = 0.014

Critical value at 5% alpha level = +1.96

Margin of Error = Critical value * Std Error = +1.96 * 0.014 = + 0.0282

confidence interval = sample proportion + margin of error

                                = 0.62 + 0.0282 = (0.592 , 0.648)