90% Confidence Interval Calculator
Provide the sample mean, sample standard deviation, and sample size to compute a 90% confidence interval for the population mean.
Z critical value (90%): 1.645
Standard error: 2.8460
Margin of error: 4.6813
Confidence interval: (120.3187, 129.6813)
How to Use This Calculator
- Enter the observed sample mean, sample standard deviation, and sample size.
- Review the standard error and margin of error for the 90% confidence level.
- Use the resulting interval to describe plausible values for the population mean.
- Ensure sample size is sufficiently large or sample distribution is approximately normal for z-based intervals.
Formula
Standard error: SE = s / √n
Margin of error: ME = zα/2 × SE
Confidence interval: x̄ ± ME
For 90% confidence, zα/2 ≈ 1.645
Full Description
A 90% confidence interval estimates a population mean when population variance is unknown but sample size is adequate. The interval spans the sample mean minus and plus the margin of error, reflecting uncertainty due to sampling variability.
Use z-based intervals when sample size is large (n ≥ 30) or when population variance is known. Consider t-distribution adjustments for small samples with unknown variance.
Frequently Asked Questions
Why use 90% instead of 95%?
90% intervals are narrower, reflecting a lower confidence level. Choose based on required certainty.
Can I use this for proportions?
This calculator focuses on means. For proportions, use the sample size and proportion formulas specific to binomial data.
What if my sample size is small?
Consider a t-distribution interval using the t critical value. Large samples or known variance justify the z critical value.
Does the interval guarantee the true mean lies within?
No. Confidence describes long-run performance; individual intervals may or may not contain the true mean.