Table of Contents
What Is a 95% Confidence Interval?
A 95% confidence interval is the most widely used confidence level in statistics, research, and scientific publications. It represents a range within which you can be 95% confident the true population parameter lies. The 5% significance level (alpha = 0.05) has become the de facto standard in most fields of science.
The 95% CI uses a z-score of 1.960 for large samples. This means the interval extends 1.96 standard errors above and below the sample mean. The 95% level strikes a balance between precision (interval width) and confidence (probability of containing the true parameter).
Formula
Worked Example
| Parameter | Value |
|---|---|
| Sample Mean | 100 |
| Standard Deviation | 15 |
| Sample Size | 50 |
| Standard Error | 15/√50 = 2.121 |
| Margin of Error | 1.960 × 2.121 = 4.158 |
| 95% CI | (95.842, 104.158) |
Interpreting 95% CI
- Correct: If we repeat this experiment many times, 95% of the calculated intervals will contain the true mean.
- Incorrect: There is NOT a 95% probability that the true mean lies in this specific interval.
- Width: Wider intervals indicate less precision; narrower intervals indicate more precision.
- Sample size effect: Increasing sample size narrows the interval (improves precision).
Frequently Asked Questions
Why is 95% the most common confidence level?
The 95% level (alpha = 0.05) was popularized by Sir Ronald Fisher as a convenient threshold for statistical significance. It balances the risk of false positives (5%) with practical utility. Most journals, regulatory bodies, and textbooks default to this level.
How can I make my confidence interval narrower?
You can narrow the interval by: (1) increasing the sample size, which reduces the standard error; (2) reducing variability in the data; or (3) using a lower confidence level (though this reduces certainty).
Does 95% CI mean 95% of the data falls in the range?
No. The confidence interval estimates the population mean, not the range of individual data points. A prediction interval would describe where individual observations are likely to fall.