determining sample size

statistics

sampling error : half the width of the confidence interval. So if you have $5\pm 3$, then 1.5 would be the sampling error.

Determing sample size for confidence interval of $\mu$

$SE=z_{\frac{\alpha }{2}}\frac{\sigma }{\sqrt{n}}$ or in terms of n: $n=(\frac{(z_{\frac{\alpha }{2}})\sigma }{(SE)}{)}^2$

Given $\sigma$ is usually unknown, you can either use $s$ (stddev from the sample) or conservatively estimate it via the range $\sigma \approx R/4$, then round up.

Determining sample size for confidence interval of $p$

$SE=\frac{z_{\alpha }}{2}\sqrt{\frac{pq}{n}}$ or in terms of n: $n=\frac{(\frac{z_{\alpha }}{2}{)}^2(pq)}{(SE{)}^2}$

Because $pq$ is unknown, we can estimate it using $\hat{p}$.

Determining margin of error

Margin of error is $ME=z_{\alpha /2}\cdot \sigma /\sqrt{n}$