Question

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. You have no preconceived idea of what that proportion might be. What sample size is needed if you wish to be 99% confident that your estimate is within 0.04 of the true​ proportion?

A sample size of ____ is needed

(Round up to the nearest whole​ number.)

Answer 1

Solution :

Given that,

= 0.5 ( use 0.5)

1 - = 1 - 0.5= 0.5

margin of error = E =0.04

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = 2.58 ( Using z table ( see the 0.005 value in standard normal (z) table corresponding z value is 2.58 )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.58 / 0.04)² * 0.5 * 0.5

=1040

Sample size = 1040

note ( when you have z value 3 decimal than Z_/2 = 2.576 so , n =1037