Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that your esimate is within 1% of the true population proportion. How large of a sample size is required? n =

Answer 1

Answer:

Given that:

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that you estimate is within 1% of the true population proportion.

E = 1% = 0.01

We have no reasonable estimate for the population proportion.In this case

take p = 0.5 and 1 - p = 0.5

Now,$\alpha = 1 - c$

a = 1-0.99

$\alpha= 0.01$

$\alpha/2 = 0.005$

$\therefore z_{\alpha/2} = 2.576$ .. (using z table)

The sample size for estimating the proportion is given by

$n=\hat{p}*(1-\hat{p})*(\frac{z_{\alpha /2}}{E})^2$

$n=0.5*(1-0.5)*(\frac{2.576}{0.01})^2$

$n=0.5*0.5*(257.6)^2$

$n=0.5*0.5*66357.76$

$n=16589$