Confidence interval (mean or proportion) API

Compute a confidence interval for a mean (x̄ ± z·s/√n) or a proportion (Wald p̂ ± z·√(p̂(1−p̂)/n)) at any confidence level, returning margin of error, lower and upper bounds. Auditable: echoes the z critical value and standard error. Answers '95% confidence interval for the mean','margin of error for this proportion','CI bounds'.

Price$0.01per request

MethodPOST

Route/v1/calc/stat-confidence-interval

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcstatisticsconfidence-intervalmargin-of-errorproportionmeanwaldinference

API URLhttps://x402.hexl.dev/v1/calc/stat-confidence-interval

Integration docs

Example request

{
  "type": "mean",
  "mean": 100,
  "sd": 15,
  "n": 36,
  "confidence": 0.95
}

Example response

{
  "type": "mean",
  "confidence": 0.95,
  "mean": 100,
  "standardError": 2.5,
  "z": 1.96,
  "marginOfError": 4.89991,
  "lower": 95.10009,
  "upper": 104.89991,
  "n": 36,
  "rating": "95% CI",
  "interpretation": "95% CI for the mean: [95.1001, 104.8999]."
}

Input schema

{
  "type": "object",
  "required": [],
  "properties": {
    "type": {
      "type": "string",
      "enum": [
        "mean",
        "proportion"
      ],
      "default": "mean"
    },
    "mean": {
      "type": "number",
      "examples": [
        100
      ]
    },
    "sd": {
      "type": "number",
      "examples": [
        15
      ]
    },
    "n": {
      "type": "number",
      "examples": [
        36
      ]
    },
    "successes": {
      "type": "number",
      "description": "for proportion: number of successes",
      "examples": [
        60
      ]
    },
    "confidence": {
      "type": "number",
      "default": 0.95,
      "examples": [
        0.95
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}