Question

In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories! Math was chosen by 222 of the 1000 as the favorite subject, and it was also chosen by 362 of the 1000 as the least favorite subject.

(a) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the favorite subject in school. (Give the answers to four decimal places.)
(  ,  )

(b) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the least favorite subject. (Give the answers to four decimal places.)
(  ,  )

You may need to use the appropriate table in Appendix A to answer this question.

Answer 1

Solution :

Given that,

n = 1000

a) x = 222

Point estimate = sample proportion = = x / n = 222 / 1000 = 0.222

  1 - = 1 - 0.222 = 0.778

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.222 * 0.778) / 1000 )

= 0.0258

A 95% confidence interval for population proportion p is ,

± E  

= 0.222  ± 0.0258

= ( 0.1962, 0.2478 )

b) x = 362

Point estimate = sample proportion = = x / n = 362 / 1000 = 0.362

  1 - = 1 - 0.362 = 0.638

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.362 * 0.638) / 1000 )

= 0.0298

A 95% confidence interval for population proportion p is ,

± E  

= 0.362  ± 0.0298

= ( 0.3322, 0.3918 )