Question

In a 2015 Gallup poll of 804 randomly selected adults living in the 50 U.S. states and the District of Columbia, 466 felt that gay and lesbian relationships were morally acceptable. Construct a 95% confidence interval for the proportion of Americans who feel that gay and lesbian relationships are morally acceptable

Answer 1

Solution :

Given that,

n = 804

x = 466

= x / n =466 / 804 = 0.580

1 - = 1 - 0.580 = 0.420

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.05 = 1.960

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

= 1.960 * (((0.580 * 0.420) / 804 )

= 0.034

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.580 - 0.034 < p < 0.580 + 0.034

0.546 < p < 0.614

The 95% confidence interval for the population proportion p is : ( 0.546 , 0.614)