Confidence Interval

Updated 28 Sep 2026

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What it is
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  an interval constructed by a procedure designed to contain the population parameter at a stated long-run rate under its assumptions
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Interpretation
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  a 95% confidence procedure covers the true parameter in approximately 95% of repeated samples under the model
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  this is not a claim that 95% of individual observations lie inside the interval
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Handout example
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  sample size $n=1082$ ; reported sample proportion $\hat p=0.65$
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  the handout reports approximately $65%\pm3$ percentage points, or 62%–68%
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Arithmetic check
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  under a simple-random-sample normal approximation, $1.96\sqrt{\hat p(1-\hat p)/n}\approx0.02842$
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  this gives approximately 62.16%–67.84%, consistent with the handout’s rounded interval
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Caution
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  this calculation does not verify the historical poll’s design, weighting, or reported survey methodology
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  confidence intervals do not automatically account for selection bias or measurement error
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Related
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  Inferential Statistics
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Linked references 3