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
Details, formula, and sources
Flags small-n cases where Wilson / Clopper-Pearson or a t-interval is more appropriate.
Proportion: 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.
Standard 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).
Universal reference; covered in any introductory statistics textbook (Moore, McCabe; Devore; OpenIntro Statistics).
Estimate 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.
Field names used by the API: mode, 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