Confidence Interval (Mean)
Interval estimate for a population mean.
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Formula
CI = x̄ ± z* × (σ/√n)
Uses z critical values (90/95/99%) and known or estimated σ. Standard error SE = σ/√n sets the margin.
Worked example
Mean 50, σ=12, n=30 at 95% gives roughly [45.7, 54.3].
Where this can give the wrong answer
- Assumes approximate normality or large n.
- Uses z not t — better for large n or known σ.
- Small n with unknown σ should use t distribution.
FAQ
- Common trade-off between width and confidence; 99% widens the interval.