95% Confidence Interval Calculator
Enter the sample mean, sample standard deviation, and sample size to compute a 95% confidence interval for the population mean.
Z critical value (95%): 1.960
Standard error: 2.8460
Margin of error: 5.5782
Confidence interval: (119.4218, 130.5782)
How to Use This Calculator
- Enter sample summary statistics.
- Review the computed standard error and margin of error.
- Interpret the resulting 95% confidence interval in the context of your study.
- Ensure assumptions (normality or large sample size) are reasonable.
Formula
SE = s / √n
ME = zα/2 × SE
CI = x̄ ± ME
For 95% confidence, zα/2 ≈ 1.960
Full Description
The 95% confidence interval is a widely used interval estimate providing a balance between precision and confidence. It assumes a normal sampling distribution of the mean, which is satisfied by large sample sizes or known population variance.
Frequently Asked Questions
Should I use t instead of z?
For small samples with unknown population standard deviation, a t-interval is recommended.
Does the interval guarantee the true mean?
No. It provides a range that would capture the true mean in 95% of repeated samples.
Can I change the confidence level?
Use the 90% or 99% confidence interval calculators for alternate confidence levels.
How do I report the results?
Present the interval (lower, upper) alongside the sample mean and context for clarity.