Confidence Interval Calculator
Find the confidence interval for a mean from the sample mean, standard deviation and sample size.
95% confidence interval
93.80830432 to 106.1916957
- Margin of error (±)
- 6.191695685
- Critical t (df = 24)
- 2.063898562
- Standard error
- 3
Show the work
Standard error of the mean
SE = s ÷ √n
15 ÷ √25 = 3
Critical t for 95% confidence (two-sided)
t with 2.5% of the curve above it, 24 degrees of freedom (n − 1) = 2.063898562
Margin of error
E = critical value × SE
2.063898562 × 3 = 6.191695685
Interval
x̄ − E to x̄ + E
100 − 6.191695685 to 100 + 6.191695685 = 93.80830432 to 106.1916957
How it works
CI = x̄ ± critical value × s ÷ √n; critical value = t(1 − α/2, n − 1) for a sample SD, z(1 − α/2) when σ is known
Questions
- How does the confidence interval calculator work?
- CI = x̄ ± critical value × s ÷ √n; critical value = t(1 − α/2, n − 1) for a sample SD, z(1 − α/2) when σ is known.
- What do I need to enter?
- Sample mean (x̄), Standard deviation, Sample size (n), Confidence level, Standard deviation is. Optional fields can be left blank.
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