Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately ˆ p = 68 % . You would like to be 99% confident that your esimate is within 0.1% of the true population proportion. How large of a sample size is required?

n=

Answer 1

Solution :

Given that,

= 0.68

1 - = 1 - 0.68= 0.32

margin of error = E =0.1% = 0.001

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 / 0.001)2 * 0.68* 0.32

=1448433

Sample size = 1448433