Confidence Interval Calculator
Calculate confidence intervals for sample means with statistical precision
Confidence Interval Calculator
About Confidence Intervals
A confidence interval provides a range of values that likely contains the true population parameter. It gives us a measure of uncertainty around our sample estimate.
•Formula
CI = x̄ ± (z × SE)
–x̄ = sample mean
–z = z-score for the confidence level
–SE = standard error of the mean
•Common Confidence Levels
90%:z = 1.645
95%:z = 1.96
99%:z = 2.576
99.9%:z = 3.291
•Interpretation
- –A 95% confidence interval means that if we repeated the sampling process many times, 95% of the intervals would contain the true population mean
- –Wider intervals indicate more uncertainty
- –Higher confidence levels result in wider intervals
- –Larger sample sizes result in narrower intervals
•Requirements
- –Sample should be randomly selected
- –Sample size should be sufficiently large (n ≥ 30) or population should be normally distributed
- –Standard error should be known or calculable