How Do You Calculate Confidence Interval

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Confidence Interval Calculator

Calculate the confidence interval for a population mean using your sample data and desired confidence level.

80% 90% 95% 98% 99%

Results

Margin of Error:
Standard Error:
Confidence Interval:

How to Calculate a Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. It provides an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The Confidence Interval Formula

To calculate the confidence interval for a population mean, use the following formula:

CI = x̄ ± (Z * (σ / √n))
  • x̄ (Sample Mean): The average value of your sample data.
  • Z (Z-score): The number of standard deviations a given proportion is away from the mean, based on the confidence level (e.g., 1.96 for 95%).
  • σ (Standard Deviation): The measure of the amount of variation or dispersion in the set of values.
  • n (Sample Size): The total number of observations in the sample.

Step-by-Step Example

Imagine you want to calculate the 95% confidence interval for the average height of a plant species based on a sample:

  1. Gather Data: Sample Mean (x̄) = 15 cm, Standard Deviation (σ) = 2 cm, Sample Size (n) = 50.
  2. Find Z-score: For a 95% confidence level, the Z-score is 1.96.
  3. Calculate Standard Error: 2 / √50 ≈ 0.2828.
  4. Calculate Margin of Error: 1.96 * 0.2828 ≈ 0.554.
  5. Determine the Range: 15 – 0.554 to 15 + 0.554 = 14.446 to 15.554.

Interpretation: We are 95% confident that the true population mean height of these plants is between 14.45 cm and 15.55 cm.

function calculateCI() { var mean = parseFloat(document.getElementById("sampleMean").value); var size = parseFloat(document.getElementById("sampleSize").value); var sd = parseFloat(document.getElementById("stdDev").value); var confLevel = parseFloat(document.getElementById("confidenceLevel").value); if (isNaN(mean) || isNaN(size) || isNaN(sd) || size <= 0) { alert("Please enter valid positive numerical values for all fields."); return; } // Mapping of Z-scores for common confidence levels var zScores = { "0.80": 1.282, "0.90": 1.645, "0.95": 1.960, "0.98": 2.326, "0.99": 2.576 }; var z = zScores[confLevel.toString()]; // Standard Error = Standard Deviation / sqrt(Sample Size) var standardError = sd / Math.sqrt(size); // Margin of Error = Z * Standard Error var marginOfError = z * standardError; // Bounds var lowerBound = mean – marginOfError; var upperBound = mean + marginOfError; // Display results document.getElementById("stdError").innerText = standardError.toFixed(4); document.getElementById("marginOfError").innerText = "± " + marginOfError.toFixed(4); document.getElementById("finalInterval").innerText = lowerBound.toFixed(4) + " to " + upperBound.toFixed(4); document.getElementById("ci-results").style.display = "block"; }

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