Plan sample size for a mean

For an approximate two-sided mean interval with known or defensibly planned σ and desired margin E, n=(zσ/E)², rounded up. A pilot estimate can inform planning but is not magically a known population SD. More variability or higher confidence increases n; a larger allowable error reduces it. The formula assumes a suitable sampling design and does not include design effects, nonresponse inflation or a finite-population adjustment unless explicitly added.