Confidence interval calculator

Open Confidence interval calculator on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.

Tool capabilities

{
  "id": "confidence-interval-calculator",
  "category": "calculators",
  "built": true,
  "requirements": "Two-sided intervals, confidence 50–99.99%, up to ten million observations. Student t intervals require at least two observations and sample SD. The z method requires known population SD. Wilson intervals model independent binary outcomes and return proportions from 0 to 1.",
  "implementation": {
    "fields": [
      {
        "key": "method",
        "label": "Interval method",
        "value": "Mean (sample SD)",
        "type": "select",
        "values": [
          "Mean (sample SD)",
          "Mean (known population SD)",
          "Proportion (Wilson)"
        ]
      },
      {
        "key": "confidence",
        "label": "Confidence level (%)",
        "value": 95,
        "type": "number",
        "min": 50,
        "max": 99.99,
        "step": "any"
      },
      {
        "key": "n",
        "label": "Sample size",
        "value": 30,
        "type": "number",
        "min": 1,
        "max": 10000000,
        "step": 1
      },
      {
        "key": "mean",
        "label": "Observed mean",
        "value": 10,
        "type": "number",
        "min": -1000000000000,
        "max": 1000000000000,
        "step": "any",
        "showWhen": {
          "method": [
            "Mean (sample SD)",
            "Mean (known population SD)"
          ]
        }
      },
      {
        "key": "sd",
        "label": "Standard deviation",
        "value": 2,
        "type": "number",
        "min": 0,
        "max": 1000000000000,
        "step": "any",
        "help": "Use sample SD for the t interval, and a genuinely known population SD for the z interval.",
        "showWhen": {
          "method": [
            "Mean (sample SD)",
            "Mean (known population SD)"
          ]
        }
      },
      {
        "key": "successes",
        "label": "Observed successes",
        "value": 15,
        "type": "number",
        "min": 0,
        "max": 10000000,
        "step": 1,
        "showWhen": {
          "method": [
            "Proportion (Wilson)"
          ]
        }
      }
    ],
    "note": "Two-sided t or z intervals for a mean, or a Wilson score interval for a binomial proportion. The t method needs at least two observations. Confidence is long-run method coverage, not a probability assigned to this fixed parameter.",
    "input": false,
    "live": true,
    "presentation": "metrics",
    "background": false,
    "inputMaxLength": 1000000,
    "inputErrorCode": "STAT_SIZE",
    "experience": {
      "automatic": true,
      "single": false,
      "inputMaxLength": 1000000,
      "inputMode": "text",
      "label": "Your text",
      "placeholder": "Type or paste your input…",
      "help": "Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.",
      "helpParts": [
        "Change the input or settings to update your result.",
        "Results update as you type.",
        "Up to 1,000,000 characters."
      ],
      "action": null
    },
    "mode": "automatic",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}

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