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 = 24 % . You would like to be 99% confident that your esimate is within 0.5% of the true population proportion. How large of a sample size is required? Show your work .

Answer 1

Solution :

Given that,

= 24% = 0.24

1 - = 1 - 0.24 = 0.76

margin of error = E = 0.5% = 0.005

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

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

   = (2.576 / 0.005)2 * 0.24 * 0.76

= 48415

sample size = n = 48415