"Do the counts in each category match what we'd expect?" Each cell contributes (O−E)²/E — bigger gaps push χ² up and the p-value down.
χ² statistic—
df—
p-value—
Decision—
Observed (O)Expected (E)
200
35%
Classic use: a die maker claims a fair die. You roll 600 times and count outcomes — expected is 100 per face. If observed is wildly off (lots of 6s, few 1s) χ² is large and you reject "fair."