Confidence Interval Simulator

Simulate margin of error and interval width from sample statistics

Sample mean

Std dev

Sample size n

Confidence

Confidence Interval Formulas

Standard error	SE = s / sqrt(n)
Margin of error	ME = critical value x SE
Interval	mean +/- ME

Step-by-Step Example

If mean = 100, standard deviation = 15, n = 36, and confidence level is 95%, then SE = 15 / sqrt(36) = 2.5. The margin of error is 1.96 x 2.5 = 4.9, so the interval is 95.1 to 104.9.

Practical Rules

Larger samples create narrower intervals.
Higher confidence levels create wider intervals.
More variation in the data increases interval width.
A confidence interval is about a population value, not an individual observation.

Frequently Asked Questions

What is a confidence interval?▼

A confidence interval is a range of plausible values for a population parameter based on sample data.

What is margin of error?▼

Margin of error is the amount added and subtracted from the sample estimate to form the interval.

How does sample size affect the interval?▼

Larger sample sizes reduce standard error and usually make the confidence interval narrower.

How does confidence level affect width?▼

Higher confidence levels require wider intervals.

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