What is a Confidence Interval?

It represents a range of values within which the true population parameter is expected to fall with a specified probability.

Confidence Interval Calculator

Calculate the confidence interval for a sample mean with standard deviation and size bounds.

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Parameters

R Reset

Sample Mean (x̄)The average value of the dataset or population.

100

-100,000100,000

Standard Deviation (s)Standard deviation. A measure of the dispersion or spread of values.

0.0110,000

Sample Size (n)

21,000,000

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95% Confidence Interval

[94.6323, 105.3677]Calculated · 100%

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Margin of Error (E)5.3677

Standard Error (SE)2.7386

Critical Value (z*)1.960

Result Interpretation

The confidence interval is [94.6323, 105.3677].

Mathematical Explanation

\text{CI} = \bar{x} \pm z^* \left(\frac{\sigma}{\sqrt{n}}\right)

With a sample mean of 100, standard deviation of 15, and size n = 30, the standard error is 2.7386. At a 95% confidence level (critical z* = 1.960), the margin of error is 5.3677. This yields a confidence range of 94.6323 to 105.3677.

How to Use the Confidence Interval Calculator

Determine the confidence interval ranges of a sample mean based on sample dimensions.

Input variables:

Sample Mean (x̄): Bounded parameter in the mathematical model.
Standard Deviation (s): Bounded parameter in the mathematical model.
Sample Size (n): Bounded parameter in the mathematical model.
Confidence Level (%): Bounded parameter in the mathematical model.

Confidence Intervals: Estimating Margins of Error in Statistics

Master standard error calculations, margins of error, and critical z-scores for 90%, 95%, and 99% confidence limits.

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