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Probability & Statistics

Statistical Thinking

Confidence Intervals: The Honest Range

7 min+70 XPStep 1/10

A point estimate is a guess; a CI is the guess with a margin

A poll reports 52% support, ±3%. That ±3% is the margin of error — the honest part of the estimate.

A 95% confidence interval says: 'intervals built this way contain the true value 95% of the time.' A range of [49%, 55%] admits the truth could sit anywhere inside — including below 50%, which is why 'too close to call' exists.

  • Wider interval → less certainty (small sample, noisy data)
  • Narrower interval → more certainty (big sample, consistent data)

A single number with no interval is pretending to know more than you do.

insight

The precise statement is subtle: '95% of intervals built this way trap the true value' — not '95% chance this interval has it.' The true value isn't random; the interval is.