Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 99% confident that you estimate is within 4% of the true population proportion. How large of a sample size is required?

Show your work please I don't understand this

Answer 1

Given that,

\hat p= 0.5 ( assume 0.5)

1 - \hat p = 1 - 0.5= 0.5

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

\alpha = 1 - 95% = 1 - 0.95 = 0.05

\alpha / 2 = 0.05 / 2 = 0.025

Z\alpha/2 = Z0.025 = 1.960 ( Using z table )

Sample size = n = (Z\alpha/2 / E)2 * \hat p * (1 - \hat p )

= (1.960 / 0.04)2 * 0.5 * 0.5

= 600.25

Sample size =601