In: Statistics and Probability
A random survey of 2000 people is made & 900 responded affirmatively (so p = 0.45). Build & interpret a 95% confidence interval.
Solution :
Given that,
n = 2000
x = 900
Point estimate = sample proportion =
= x / n = 900/2000=0.45
1 -
= 1- 0.45 =0.55
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 ( Using z table )
Margin of error = E = Z/2 *
(((
* (1 -
)) / n)
= 1.96 (((0.45*0.55)
/2000 )
E = 0.022
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.45-0.022 < p < 0.45+0.022
0.428< p < 0.472