Mistake Master
Inside Means Plausible. It Has Never Meant Proven
You'll learnhow to judge a claim by where it falls relative to an interval, why a value inside is only un-excluded and a value outside is only unsupported, what a straddling interval does and does not settle — measured against how often it appears when a real majority exists — and how to write the three-part justification that survives grading.
A confidence interval is a list of plausible values for the parameter, and that one sentence decides every claim it can judge. A claimed value inside has not been ruled out; a claimed value outside is contradicted by these data; neither is proof. This page measures what those hedges are worth. Suppose 52% of a district really does support a measure — a genuine majority. A poll of 400 returns an interval that straddles 0.50, and therefore cannot call the majority, 87.2% of the time: reading that undecided result as evidence of no majority is wrong about seven times in eight. Suppose instead the split is exactly 50-50. Then 5.1% of samples produce intervals that exclude 0.50 outright, contradicting a claim that is perfectly true. And one poll on this page — 220 of 400 — supports a majority at 95% confidence and declines to at 99%, on identical data.