Most people think a 95% confidence interval means "95% chance the true value is inside." Wrong. It means if you repeated the sampling forever, 95% of your intervals would capture the truth. Drag the slider to see how sample size changes the width of the interval.
Interval Width
n = 30
Population mean μ = 100, σ = 15
95% CI: [94.6, 105.4]
Sample Size (n)
1050100150200
Width
10.8
Margin ±
5.4
For large samples with known population standard deviation, the interval formula is x̄ ± z* × (σ/√n). The z-critical value comes from the normal distribution — for 95% confidence, z* = 1.96. As sample size increases, the denominator √n gets larger, so the margin of error shrinks. This is why bigger samples give tighter, more precise intervals. The confidence level stays at 95%, but the interval narrows because we have more data.
Know This
Wider confidence intervals result from higher confidence levels, smaller sample sizes, or greater population variability — all three factors increase uncertainty in your estimate.