Estimating pizza preference from a sample of 30
A school has six hundred students. We want to know how many prefer pizza for lunch — but we can't ask all six hundred!
So we take a random sample — thirty students picked at random.
Eighteen of those thirty students say they prefer pizza.
That gives us a sample fraction: eighteen out of thirty.
Eighteen over thirty simplifies to sixty percent.
We infer the same proportion for the whole school: sixty percent of six hundred is three hundred sixty students.
Here's the catch — a different random sample can give a different estimate.
Sample two finds fifteen out of thirty. That's fifty percent — about three hundred students.
Sample three finds twenty-one out of thirty. That's seventy percent — about four hundred twenty.
Estimates vary from sample to sample, but they cluster near the true value. More samples give us a better picture!