In: Statistics and Probability
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”.
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 = Z0.025 = 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)