In: Statistics and Probability
A large earthquake hit a city in South America. A survey of 2,000 houses found that 600 of them had collapsed. Construct and interpret a 95% confidence interval for the proportion of collapsed houses.
Solution :
Given that,
n = 2000
x = 600
Point estimate = sample proportion =
= x / n = 600/2000=0.3
1 -
= 1- 0.3 =0.7
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 (((0.3*0.7)
/ 2000)
E = 0.02
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.3-0.02 < p < 0.3+0.02
0.28< p < 0.32