99% Confidence Interval Calculator
Enter the sample mean, standard deviation, and sample size to obtain a 99% confidence interval for the population mean.
Z critical value (99%): 2.576
Standard error: 2.8460
Margin of error: 7.3309
Confidence interval: (117.6691, 132.3309)
How to Use This Calculator
- Enter sample statistics (mean, standard deviation, size).
- Review the standard error and margin of error for the 99% confidence level.
- Use the interval to describe plausible values for the population mean.
- Verify that z-based assumptions (large sample or known variance) are satisfied.
Formula
SE = s / √n
ME = zα/2 × SE
CI = x̄ ± ME
For 99% confidence, zα/2 ≈ 2.576
Full Description
A 99% confidence interval provides a wider range than 90% or 95% intervals, reflecting higher certainty demands. It is useful when minimizing Type I errors or when presenting conservative estimates.
Frequently Asked Questions
Why is the interval wider?
Higher confidence requires capturing more of the sampling distribution, increasing the margin of error.
Can I use this for small samples?
For small samples with unknown variance, use t-based intervals instead of z-based.
Does this assume normality?
As with other z-intervals, it assumes either known variance or a large sample size to justify normal approximations.
How do I interpret the interval?
It conveys a range that would contain the true mean in 99% of samples drawn in the same way.