📏 Confidence Interval & Margin of Error

Select a scenario (mean with known σ, mean with unknown σ, or sample proportion), supply your sample statistics, and receive a confidence interval with supporting insights and interpretation.

1. Select Scenario

Mean (σ known) Mean (σ unknown, use s) Proportion

Confidence Level

2. Provide Sample Information

Sample Mean (x̄)

σ (population) or s (sample)

For σ known scenario, enter population σ; otherwise provide sample s.

Sample Size (n)

3. Results

Point Estimate

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Margin of Error

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Lower Bound

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Upper Bound

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Interpretation

No interval calculated yet.

Insights

No values analysed yet.

Formula Reference

Mean (σ known): \( \bar{x} \pm z_{α/2} \frac{σ}{\sqrt{n}} \)
Mean (σ unknown): \( \bar{x} \pm t_{α/2, n-1} \frac{s}{\sqrt{n}} \)
Proportion (Wilson): \( \frac{p̂ + \frac{z^2}{2n} \pm z\sqrt{\frac{p̂(1-p̂)}{n} + \frac{z^2}{4n^2}}}{1 + \frac{z^2}{n}} \)