Confidence Interval (Proportion or Mean)
Wald z-interval for a sample proportion or a sample mean.
Example
You enter
- Mode proportion
- Sample size n 100
- Sample proportion (0 to 1) 0.6
- Confidence level 95
You get
- z critical (two-tailed) 1.96
- Standard error 0.04899
- Margin of error 0.096
- Lower bound 0.504
- Upper bound 0.696
Checked against published worked examples from: Wald (1943), standard inferential statistics.
Details, formula, and sources
ScopeFlags small-n cases where Wilson / Clopper-Pearson or a t-interval is more appropriate.
Formula or tableProportion: phat +/- z * sqrt(phat*(1-phat)/n). Mean: xbar +/- z * (sd / sqrt(n)). z critical values (two-tailed) from the standard normal: 80% = 1.2816, 90% = 1.6449, 95% = 1.9600, 98% = 2.3263, 99% = 2.5758.
Source and editionStandard inferential statistics. Wald CI per Wald, Abraham, 'Tests of statistical hypotheses concerning several parameters when the number of observations is large,' Trans. Amer. Math. Soc. 54 (1943).
Free accessUniversal reference; covered in any introductory statistics textbook (Moore, McCabe; Devore; OpenIntro Statistics).
What governsEstimate only. Readability formulas and similar metrics are derived from a representative population and have known edge-case noise. The classroom teacher governs final text selection, grade placement, and assessment decisions.
API field namesmode, n, proportion, confidence_pct, z_critical, standard_error, margin_of_error, lower_bound, upper_bound
- Two-tailed z critical values are two-tailedconvention
- Independence sample observations are assumed independent and identically distributedWald CI assumption
- Continuity correction not appliedthis tile is the Wald form; a continuity-corrected variant exists but is not bundled