Confidence Interval Calculator
Calculate confidence intervals for population means and proportions.
95% Confidence Interval Calculator
Lower Bound
48.0400
Upper Bound
51.9600
Point Estimate
50.0000
Margin of Error
± 1.9600
Interval Visualization
48.0450.0051.96
Details
Standard Error1.000000
Critical Value (z)1.9600
What is a Confidence Interval?
A confidence interval is a range of values that likely contains the true population parameter. A 95% CI means that if we take many samples, approximately 95% of the intervals will contain the true value.
Correct Interpretation
A 95% CI does NOT mean there's a 95% probability that the parameter is in the interval. The parameter is fixed; it's the interval that varies across samples.
Factors Affecting Width
The interval becomes narrower with: larger sample size, lower variability, or lower confidence level. There's a trade-off between precision and confidence.