Confidence Interval Calculator
Calculate confidence intervals for population means and proportions with margin of error
Results
Enter values and click Calculate to see the result.
Theory & Formula
Theory
A confidence interval provides a range of plausible values for a population parameter based on sample data. The confidence level (e.g., 95%) indicates that if we repeated the sampling process many times, approximately that percentage of intervals would contain the true population parameter.
Confidence Interval for Mean
Use z (normal) for large samples (n ≥ 30) or known population σ. Use t (t-distribution) for small samples (n < 30) with unknown σ.
Confidence Interval for Proportion
Requires np̂ ≥ 5 and n(1-p̂) ≥ 5 for normal approximation to be valid.
Interpretation
A 95% confidence interval means: "We are 95% confident that the true population parameter lies within this interval." This does NOT mean there is a 95% probability the parameter is in this specific interval - the parameter is fixed, but our interval estimate varies from sample to sample.
Example
A survey of 100 students found an average study time of 5 hours per week with a standard deviation of 1.5 hours. The 95% confidence interval is approximately [4.71, 5.29] hours, meaning we are 95% confident the true average study time for all students is between 4.71 and 5.29 hours per week.