95% CI for a mean — formula and interpretation.

easy

Answer

$t_{n - 1, \;0.975}\; \cdot \;(s\; / \; \sqrt n)$
$Interpretation: if we repeated the experiment many times, 95% of the CIs would contain the true μ.$
$NOT: 'there's a 95% chance μ is in this specific interval' (that's Bayesian credible interval language).$
$For large n, t \approx z = 1.96.$
$Foundational for A/B testing and any point estimate reporting.$

Check yourself — multiple choice

μ has 95% chance to be here
X̄ ± $t_{n - 1, \;0.975}$ · s/√n; frequentist: 95% of such CIs cover the true μ across repeated experiments
Same as prediction
Only Bayesian

95% CI: X̄ ± t·SE; frequentist coverage interpretation.

#confidence-interval

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