Confidence Interval Calculator
Calculate confidence intervals to estimate population parameters with statistical certainty.
Input Parameters
Results
95% Confidence Interval
[46.4215, 53.5785]
Range where true population mean likely falls
Lower Bound
46.4215
Upper Bound
53.5785
Margin of Error (±)
3.5785
Standard Error
1.8257
Z-Score
1.96
Understanding Confidence Intervals
A confidence interval provides a range of values that likely contains the true population parameter. It combines point estimate (sample mean) with margin of error to show estimation uncertainty.
Interpretation
A 95% confidence interval means: If we repeated this sampling process many times, 95% of the calculated intervals would contain the true population mean.
Formula
CI = x̄ ± (Z × σ/√n)
- x̄: Sample mean
- Z: Z-score for desired confidence level
- σ: Standard deviation
- n: Sample size
Example
Testing average response time: Sample mean = 50ms, Std Dev = 10ms, n = 30, 95% confidence.
- CI: [46.42, 53.58]
- Interpretation: We're 95% confident the true average response time is between 46.42ms and 53.58ms