Question

An article summarized results from a national survey of 2302 Americans age 8 to 18. The sample was selected in a way that was expected to result in a sample representative of Americans in this age group.

(a) Of those surveyed, 1329 reported owning a cell phone. Use this information to construct a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone. (Round your answers to three decimal places.)

( , )

(b) Of those surveyed, 1621 reported owning an MP3 music player. Use this information to construct a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player. (Round your answers to three decimal places.)

( , )

Answer 1

solution:-
given that n = 2302

(a)here given x = 1329

proportion p = x/n = 1329/2302 = 0.577

90% confidence for Z is 1.645

confidence interval formula for proportion

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.577 +/- 1.645 * sqrt(0.577*(1-0.577)/2302)

=> 0.577 +/- 0.017

=> (0.560 , 0.594)

(b)here given x = 1621

proportion p = x/n = 1621/2302 = 0.704

90% confidence for z is 1.645

confidence interval formula for proportion

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.704 +/- 1.645 * sqrt(0.704*(1-0.704)/2302)

=> 0.704 +/- 0.016

=> (0.688 , 0.720)