Question

Determine the required sample size if you want to be 99% confident that the sample proportion is within 2% of the population proportion if no preliminary estimate of the true population is available.

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =2 % = 0.02

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

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

= (2.58 / 0.02)2 * 0.5 * 0.5

=4160.25

Sample size = 4161

( when you have z value 3 decimal answer z=2.576=n=4147.36=4148