What is a confidence interval?

A confidence interval gives a range of values within which we're confident the true population parameter lies. A 95% CI means if we repeated the study many times, 95% of intervals would contain the true value.

What is margin of error?

Margin of error is half the width of the confidence interval. It represents the maximum expected difference between the sample statistic and the population parameter.

How does sample size affect CI?

Larger samples produce narrower confidence intervals (more precision). Doubling sample size reduces the margin of error by about 30% (factor of √2).

90% vs 95% vs 99% confidence?

Higher confidence levels produce wider intervals. 99% CI is wider than 95%, which is wider than 90%. There's a trade-off between confidence and precision.

When to use Z vs t distribution?

Use Z when population standard deviation is known OR sample size is large (n ≥ 30). Use t-distribution for smaller samples with unknown population SD.

Confidence Interval Calculator

Calculate confidence intervals for population means.

Sample Mean (x̄)

Standard Deviation (σ or s)

Sample Size (n)

Confidence Level

Confidence Interval

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95% Confidence Interval

(0, 0)

75 ± 0

Lower Bound

Upper Bound

Margin of Error

Standard Error

Calculation Steps

1. Z-critical for 95% = 0

2. Standard Error = σ/√n = 10/√100 = 0

3. MOE = Z × SE = 0 × 0 = 0

4. CI = x̄ ± MOE = 75 ± 0 = (0, 0)

Documentation

Confidence Intervals

A confidence interval provides a range estimate for a population parameter based on sample data. The width depends on sample size, variability, and desired confidence level.

MOE

Frequently Asked Questions

About the Confidence Interval

What it calculates

This confidence interval solves mathematical and statistical problems using standard formulas. Calculate confidence intervals for means and proportions.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Confidence Interval.

Explore More

Confidence Interval Calculator

Confidence Level

Confidence Interval

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(0, 0)

Calculation Steps

Confidence Intervals

About the Confidence Interval

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Margin of Error

Sample Size

Standard Error

ANOVA (One-Way)

Bayes Theorem Calculator

Beta Distribution