Answer to Question #199175 in Statistics and Probability for Kathrine

Question

Data from a representative sample were used to estimate that 32% of all computer users in a recent year had tried to get on a Wi-Fi network that was not their own in order to save money. You decide to conduct a survey to estimate this proportion for the current year. What is the required sample size if you want to estimate this proportion with a margin of error of 0.04? Calculate the required sample size first using 0.32 as a preliminary estimate of p.

Answer 1

Margin of error:

$ME=Z_{\alpha}\sqrt{\frac{p(1-p)}{n}}=0.04$

where n is sample size,

p is estimated proportion.

Then:

$n=\frac{Z^2_{\alpha }p(1-p)}{ME^2}$

For example, for confidence interval 95%:

$Z_{0.95}=1.96$

$n=\frac{1.96^2\cdot0.32(1-0.32)}{0.04^2}=522.45$

So, the required sample size:

$n=523$