Confidence Interval Calculator

Confidence Interval Calculator

Calculate statistical significance and margin of error instantly

80% 90% 95% 98% 99%

Calculation Summary

Margin of Error: –

Confidence Interval: –

Lower Bound: –

Upper Bound: –

function calculateCI() { var mean = parseFloat(document.getElementById('sampleMean').value); var n = parseFloat(document.getElementById('sampleSize').value); var sd = parseFloat(document.getElementById('stdDev').value); var cl = parseFloat(document.getElementById('confLevel').value); if (isNaN(mean) || isNaN(n) || isNaN(sd) || n <= 0) { alert("Please enter valid positive numbers for all fields."); return; } var zScores = { "80": 1.282, "90": 1.645, "95": 1.96, "98": 2.326, "99": 2.576 }; var z = zScores[cl.toString()]; var standardError = sd / Math.sqrt(n); var marginOfError = z * standardError; var lowerBound = mean – marginOfError; var upperBound = mean + marginOfError; document.getElementById('marginResult').innerHTML = "± " + marginOfError.toFixed(4); document.getElementById('rangeResult').innerHTML = lowerBound.toFixed(4) + " to " + upperBound.toFixed(4); document.getElementById('lowerResult').innerHTML = lowerBound.toFixed(4); document.getElementById('upperResult').innerHTML = upperBound.toFixed(4); document.getElementById('interpretationText').innerHTML = "Interpretation: We are " + cl + "% confident that the true population mean falls between " + lowerBound.toFixed(4) + " and " + upperBound.toFixed(4) + "."; document.getElementById('ci-result-container').style.display = "block"; }

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Understanding the Confidence Interval Calculator

In the world of statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter. Because researchers rarely have access to data from an entire population, they use sample data to estimate characteristics. This calculator helps you determine the precision of those estimates.

Key Components Explained

• Sample Mean (x̄): The average value found in your data sample.
• Sample Size (n): The total number of observations or participants in your study. Larger sample sizes generally lead to narrower (more precise) confidence intervals.
• Standard Deviation (s): A measure of how spread out the numbers are in your sample. A higher standard deviation indicates more variability.
• Confidence Level: Usually set at 95%, this represents how often the calculated interval would contain the true population mean if you were to repeat the experiment many times.

The Confidence Interval Formula

CI = x̄ ± Z * (s / √n)

Where:

• x̄ is the sample mean
• Z is the Z-score corresponding to your chosen confidence level
• s is the standard deviation
• n is the sample size

Practical Example

Imagine a coffee company wants to know the average caffeine content in their "Hyper-Brew" blend. They test a sample of 50 cups and find a mean caffeine content of 150mg with a standard deviation of 10mg. Using a 95% confidence level:

1. Mean (x̄): 150
2. n: 50
3. SD (s): 10
4. Z-score: 1.96 (for 95%)

The resulting Margin of Error would be approximately 2.77mg. This means the 95% Confidence Interval is 147.23mg to 152.77mg. The company can be 95% sure that the true average caffeine content for all cups produced falls within this range.

Why Use This Calculator?

Whether you are performing academic research, quality control in manufacturing, or A/B testing for a website, knowing the confidence interval is crucial for making data-driven decisions. It prevents over-reliance on a single sample mean and provides a clear picture of the potential error inherent in your data.