Sample Size & Margin of Error Planner

By the Central Limit Theorem, the sample mean distribution converges...

This planner answers one question: how many people must you ask to pin a percentage down to a chosen margin of error? Because the margin shrinks with the square root of the sample size, buying twice the precision costs four times the respondents — moving from ±3% to ±1.5% roughly quadruples n. When the expected proportion is unknown, set p = 0.5: that maximizes p(1−p) and gives the largest, safest sample size.

The margin-of-error formula measures only random sampling error — it assumes every respondent was chosen at random. In 1936 the Literary Digest polled about 2.4 million people and confidently predicted Landon would beat Roosevelt; George Gallup called it correctly with barely 50,000. The Digest's list over-sampled car and telephone owners during the Depression, so a huge but biased sample lost to a small representative one. No sample size can fix a skewed sampling frame.