Question

An urban economist wishes to estimate the proportion of Americans who own their homes. What sample size should be obtained if he wishes the estate to be within 0.03 with 99% confidence level

A: he uses a 2010 estimate of 0.723 obtained from the us census bureau?

b: he dose not use any prior estimates.

Answer 1

Solution :

Given that,

A) = 0.723

1 - = 1 - 0.723 = 0.277

margin of error = E = 0.03

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = Z _0.005 = 2.576

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= ( 2.576 / 0.03 )² * 0.723 * 0.277

= 1476.61

sample size = n = 1477

B) = 1 - = 0.5

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= ( 2.576 / 0.03 )² * 0.5 * 0.5

= 1843.27

sample size = n = 1844