Confidence Interval T Test Guide
What This Calculator Does
A t based confidence interval estimates a population mean when the population standard deviation is unknown. It uses the sample mean, sample standard deviation, sample size, and a critical value from the t distribution. The interval shows a practical range for the true mean, not a guaranteed location for one future value.
Input Choices
This calculator supports two entry styles. You can paste raw observations, or you can enter summary statistics. Raw data is useful when you want the page to compute the mean and standard deviation. Summary mode is faster when those values already come from software, a lab sheet, or a class problem.
Confidence Level Meaning
The confidence level controls interval width. A higher level needs a larger critical value. That makes the margin of error wider. A larger sample size usually makes the standard error smaller. That gives a tighter interval, if the sample spread stays similar. A larger standard deviation increases uncertainty and widens the interval.
Test Output
The tool also includes a one sample t test. Enter a hypothesized mean to compare against your sample. The t statistic measures how many standard errors separate the sample mean from that value. The p value is calculated for two tailed, left tailed, or right tailed alternatives. The decision uses the same alpha level implied by the selected confidence level.
Reading the Details
Use the diagnostic output carefully. Degrees of freedom equal sample size minus one. The standard error equals sample standard deviation divided by the square root of sample size. The margin of error is the critical t value multiplied by the standard error. These pieces explain why the final bounds move when inputs change.
Assumptions
A t interval works best with independent observations. Small samples should come from data that is roughly normal. Larger samples are more forgiving, but extreme outliers can still distort the mean and standard deviation. Always review your data source before interpreting results.
Saving Results
The CSV and PDF buttons help save the final calculation. They are useful for reports, homework, audits, and repeated quality checks. Keep the input data with your saved output so another person can reproduce the result.
Paired Data Note
For paired studies, enter the differences between pairs, not both original columns. Then treat those differences as one sample of changes for valid inference.