Question

In a December 2012 poll of 1002 American adults, 802 thought that if nothing is done to reduce global warming in the future, it would be a serious problem for the United States. Construct a 95% confidence interval for the proportion of American adults who describe this problem as “serious”.

Answer 1

Solution :

Given that,

n = 1002

x = 802

= x / n =802 /1002 = 0.800

1 - = 1 - 0.800 = 0.200

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.800 * 0.200) / 1002) = 0.0248

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.800 -  0.0248 < p < 0.800 + 0.0248

0.7752 < p < 0.8248

The 95 % confidence interval for the population proportion p is : ( 0.7752 ,  0.8248)