Question

The Pew Research Center has conducted extensive research on the young adult population (Pew Research website, November 6, 2012). One finding was that 93% of adults aged 18 to 29 use the Internet. Another finding was that 21% of those aged 18 to 28 are married. Assume the sample size associated with both findings is 500.

a. Develop a 95% confidence interval for the proportion of adults aged 18 to 29 who use the Internet.

b. Develop a 99% confidence interval for the proportion of adults aged 18 to 28 who are married.

Answer 1

a)

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.93 - 1.96 * sqrt( 0.93 * 0.07 / 500) < p < 0.93 +1.96 * sqrt( 0.93 * 0.07 / 500)

0.908 < p < 0.952

95% CI is ( 0.908 , 0.952 )

b)

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.21 - 1.96 * sqrt( 0.21 * 0.79 / 500) < p < 0.21 +1.96 * sqrt( 0.21 * 0.79 / 500)

0.174 < p < 0.246

95% CI is ( 0.174 , 0.246 )