Question

Same-sex marriage: In a recent ABC News/Washington Post poll, 1260 adults nationwide answered the question, “Overall, do you support or oppose allowing gays and lesbians to marry legally?” Of the respondents, 494 support same-sex marriage. What is the 95 % confidence interval for the proportion of all American adults who support same-sex marriage? http://www.washingtonpost.com/page/2010-2019/WashingtonPost/2015/04/23/National-Politics/Polling/release_395.xml

A-(0.365, 0.419)

B-(0.378, 0.406)

C-(0.369, 0.415)

D-(0.357, 0.427)

Answer 1

Solution :

=> Answer : Option A- (0.365 , 0.419)

Given that x = 494 , n = 1260

=> p = x/n = 494/1260 = 0.392

=> q = 1 - p = 0.608

=> for 95% confidence interval , Z = 1.96

=> The 95% confidence interval for the proportion is

=> p +/- Z*sqrt(p*q/n)

=> 0.392 +/- 1.96*sqrt(0.392*0.608/1260)

=> (0.365 , 0.419)