In: Statistics and Probability
In a poll of 120 registered voters 100 said that they supported requiring background checks for all gun buyers. Find an 85% confidence interval for the population mean and the margin of error
Solution :
Given that,
n = 120
x = 100
Point estimate = sample proportion =
= x / n = 100/120=0.833
1 -
= 1-0.833 =0.167
At 85% confidence level the z is ,
= 1 - 85% = 1 - 0.85 = 0.15
/ 2 = 0.15 / 2 = 0.075
Z/2
= Z 0.075 =1.440 Using z table )
Margin of error = E = Z/2 *
(((
* (1 -
)) / n)
= 1.440 (((0.833*0.167)
/120 )
E = 0.049
A 85% confidence interval is ,
- E < p <
+ E
0.833- 0.049 < p < 0.833+0.049
0.784< p < 0.882