A large earthquake hit a city in South America. A survey of 2,000 houses found that...

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.

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Expert Solution

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 * $\sqrt$ ((( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((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

orchestra answered 1 year ago

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