Question

Same-sex marriage: In a recent ABC News/Washington Post poll, 1377 adults nationwide answered the question, “Overall, do you support or oppose allowing gays and lesbians to marry legally?”

Of the respondents, 476 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

1. (0.321, 0.371)
2. (0.333, 0.358)
3. (0.325, 0.367)
4. (0.313, 0.379)

Answer 1

Solution :

Given that,

n = 1377

x = 476

Point estimate = sample proportion = = x / n = 476/1377=0.346

1 - = 1-0.346=0.654

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )   

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

= 1.96 (((0.346*0.654) / 1377)

E = 0.0251

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.346-0.0251 < p <0.346+ 0.0251

0.321< p < 0.371

The 95% confidence interval for the population proportion p is : 0.321, 0.371