Confidence Interval Calculator
Confidence interval for a meanRuns locally · nothing uploaded
Confidence interval
[ 69.3634 , 75.6366 ]
Margin of error (±)
3.1366
Standard error
1.5336
t critical value (df = 29)
2.0452
How it works
When to use it
- Estimate a range for the population mean from sample data.
- Report “mean ± margin of error” in a lab report or paper.
Formula
SE = s ÷ √nCI = x̄ ± t × SEt is the critical value with n − 1 degrees of freedom; it approaches z for large n.
Worked example
Given: Mean 72.5, SD 8.4, n = 30, 95% confidence
- SE = 8.4 ÷ √30 ≈ 1.5336.
- t(29) ≈ 2.0452.
- Margin = 2.0452 × 1.5336 ≈ 3.137.
Result: 95% CI ≈ 69.36 to 75.64.
Reading the result
- If you repeated the sampling many times, about 95% of such intervals would contain the true mean.
- Quadrupling n roughly halves the width.
Limitations
- Assumes a random sample and roughly normal data; unreliable for small, skewed samples.
- For means only; proportions need a different formula.
How to use
- 1Enter the sample mean, standard deviation and sample size.
- 2Choose the confidence level.
- 3Read the interval, standard error and critical value.
FAQ
Why the t-distribution?
When the population SD is unknown and estimated from the sample, use t with n−1 degrees of freedom.
What is the formula?
mean ± t* × s / √n, where s / √n is the standard error.