90% Confidence Interval Calculator

Understanding the 90% Confidence Interval and Two-Tailed T-Test

Statistical analysis relies heavily on estimating population parameters using sample data. When population variance is unknown and sample sizes are small, the Student's t-distribution provides the appropriate probability framework. A 90 percent confidence interval gives a range of values that you can be 90% confident contains the true population mean. By utilizing a two-tailed t-test architecture, this calculator accounts for discrepancies in both directions—higher or lower than the anticipated population parameter value.

Formula Used

The calculation is executed using the standard t-interval formula:

CI = $\bar{x}$ $\pm$ ($t_{\alpha/2, df}$ $\times$ ($s$ / $\sqrt{n}$))

Where $\bar{x}$ represents the sample mean, $t$ is the critical value for a two-tailed test at a 0.10 significance level, $s$ is the sample standard deviation, and $n$ represents the total sample size.

How to Use This Calculator

Using this tool is straightforward and intuitive. First, select whether you want to input raw comma-separated data values or pre-calculated summary statistics like mean and standard deviation. Next, configure your rounding precision and export preferences. Finally, click the calculate button to instantly review your precise confidence bounds rendered cleanly above the form interface.

Frequently Asked Questions