Table of Contents
What Is a 90% Confidence Interval?
A 90% confidence interval is a range of values that you can be 90% confident contains the true population parameter. This means that if you were to repeat the sampling process many times and compute a 90% CI each time, approximately 90% of those intervals would contain the true population mean.
The 90% confidence level uses a z-score of 1.645 (for large samples or known population standard deviation). It provides a narrower interval than 95% or 99% confidence levels, making it useful when slightly less certainty is acceptable in exchange for greater precision.
Confidence Interval Formula
Common Z-Values
| Confidence Level | Z-Score | Alpha (α) |
|---|---|---|
| 80% | 1.282 | 0.20 |
| 85% | 1.440 | 0.15 |
| 90% | 1.645 | 0.10 |
| 95% | 1.960 | 0.05 |
| 99% | 2.576 | 0.01 |
When to Use a 90% Confidence Interval
- Preliminary studies: When you need a quick estimate and can tolerate more uncertainty.
- Large samples: With large sample sizes, even 90% CI provides a narrow, useful range.
- Cost constraints: When the cost of being wrong is moderate, 90% confidence suffices.
- Environmental studies: Some regulatory standards accept 90% confidence levels.
Frequently Asked Questions
What does 90% confidence mean?
It means that if you repeated your study 100 times with new random samples, approximately 90 of the resulting confidence intervals would contain the true population mean. It does NOT mean there is a 90% probability the true mean is in your specific interval.
Is a 90% CI wider or narrower than 95%?
A 90% CI is narrower than a 95% CI. Lower confidence requires less margin of error, resulting in a more precise but less certain interval. The 90% CI z-score (1.645) is smaller than the 95% z-score (1.960).
When should I use z vs t distribution?
Use the z-distribution when the population standard deviation is known or the sample size is large (n > 30). Use the t-distribution for small samples with unknown population standard deviation.