In: Statistics and Probability
120 people are polled and 90 of them say they support labeling foods that contain GMO’s. Build the 90% confidence interval for the true proportion of people that support labeling foods that contain GMO’s.
Solution :
Given that,
n = 120
x = 90
Point estimate = sample proportion =
= x / n = 90/120=0.75
1 -
=0.25
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645 ( Using z table )
Margin of error = E Z/2
*
((
* (1 -
)) / n)
= 1.645 *((0.75*0.25)
/120 )
E = 0.065
A 90% confidence interval for population proportion p is ,
- E < p <
+ E
0.75-0.065 < p < 0.75+0.065
0.685< p < 0.815