In: Statistics and Probability
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n equals 922 and x equals 557 who said "yes." Use a 99 % confidence level.
Solution :
Given that,
n = 922
x = 557
Point estimate = sample proportion =
= x / n = 557/922=0.604
1 -
= 1- 0.604 =0.396
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 =
0.01
/ 2 = 0.01 / 2 = 0.005
Z/2
= Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z
/ 2 * (
(((
* (1 -
)) / n)
= 2.576* (((0.604*0.396)
/922 )
E = 0.0415
A 99% confidence interval for population proportion p is ,
- E < p <
+ E
0.604-0.0415 < p <0.604+ 0.0415
0.5625< p < 0.6455
The 99% confidence interval for the population proportion p is :lower limit= 0.5625,upper limit= 0.6455