Calculate confidence intervals for a population mean (known or unknown σ) and population proportion at various confidence levels.
Use z-distribution when population standard deviation σ is known.
| Property | Value |
|---|---|
| Sample mean (x̄) | 50 |
| Critical value (z*) | 1.96 |
| Standard Error (σ/√n) | 1.8257 |
| Margin of Error | ±3.5785 |
| Lower bound | 46.4215 |
| Upper bound | 53.5785 |
| Confidence Level | z* | α |
|---|---|---|
| 80% | 1.2816 | 0.200 |
| 85% | 1.4395 | 0.150 |
| 90% | 1.6449 | 0.100 |
| 95% | 1.96 | 0.050 |
| 99% | 2.5758 | 0.010 |
| 99.5% | 2.807 | 0.005 |
| 99.9% | 3.2905 | 0.001 |
Calculate confidence intervals for sample means or proportions with our free calculator, useful for statistics coursework, research, and data analysis.
For a sample mean: CI = x̄ ± z × (σ/√n), where x̄ is the sample mean, z is the z-score for your confidence level, σ is the standard deviation, and n is sample size. Higher confidence levels (like 99% vs 95%) produce wider intervals.
It means that if you repeated your sampling process many times, approximately 95% of the calculated intervals would contain the true population parameter, it's a statement about the method's reliability, not a probability about this specific interval.
To be more confident the interval captures the true value, you need to cast a wider net, there's a direct trade-off between confidence level and precision.
The formulas differ slightly, proportions use a different standard error calculation based on the proportion itself, since proportions have a different underlying distribution than continuous means.
Yes, larger samples produce narrower (more precise) confidence intervals, since more data reduces the standard error.