Confidence Interval Calculator
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Calculation Type
Sample Information
Confidence Intervals
- • Higher confidence levels result in wider intervals
- • Larger sample sizes result in narrower intervals
- • The interval contains the true parameter with the specified confidence
- • Check assumptions before interpreting results
Confidence Interval
(94.632, 105.368)
95% confidence
Margin of Error
5.368
±
Interval Width
10.735
Total width
Sample Statistic
100.000
Point estimate
Standard Error
2.739
SE
Distribution Information
Distribution:normal
Critical Value:1.960
Parameters: μ = 100, σ = 15
Sample Size Analysis
Current sample size:30 (Moderate)
Sample sizes needed for different interval widths:
Width ±0.5:n = 461
Width ±1:n = 116
Width ±2:n = 29
Width ±5:n = 5
How it works
A confidence interval gives a range that likely contains the true population value, based on your sample. It centers on the sample mean and extends a margin of error on each side, set by the confidence level, the variability in the data, and the sample size.
Confidence interval for a mean
CI = mean ± z · (σ ÷ √n)
- z
- z-score for the confidence level (1.96 for 95%)
- σ
- standard deviation
- n
- sample size
Worked example
- Mean = 100, σ = 15, n = 36
- 95% confidence (z = 1.96)
- Margin = 1.96 × (15 ÷ √36) = 1.96 × 2.5
- = 4.9
95% CI: 100 ± 4.9 → (95.1, 104.9).
Good to know
- A larger sample shrinks the interval — precision improves with √n, so 4× the data halves the margin.
- 95% confidence means that if you repeated the study many times, ~95% of such intervals would contain the true value.
- Use the t-distribution instead of z for small samples or unknown population variance.