Single T Test Confidence Interval Calculator

Formula Used

The one sample t statistic is calculated as:

t = (x̄ - μ₀) / (s / √n)

Here, x̄ is the sample mean. μ₀ is the hypothesized mean. s is the sample standard deviation. n is the sample size.

The degrees of freedom are:

df = n - 1

The two sided confidence interval is:

x̄ ± t* × (s / √n)

The calculator also computes p value, standard error, margin of error, Cohen d, and Hedges g.

How to Use This Calculator

1. Choose raw data if you have all observations.
2. Choose summary values if you know n, mean, and standard deviation.
3. Enter the hypothesized mean for the t test.
4. Select the confidence level and alternative hypothesis.
5. Choose the confidence interval type.
6. Press Calculate to show results below the header.
7. Use CSV or PDF export for saving reports.

Example Data Table

About the Single T Test Confidence Interval Calculator

A single t test studies one sample mean. It compares that mean with a chosen value. The chosen value is often a target, standard, claim, or past average. This calculator also builds a confidence interval. The interval shows a likely range for the true population mean.

When to Use It

Use this tool when the population standard deviation is unknown. That is common in real research. Enter raw data when you have every observation. Use summary mode when you already know the sample size, mean, and sample standard deviation. The calculator supports two sided, greater than, and less than tests.

What the Results Mean

The t statistic measures distance from the hypothesized mean. It uses standard errors as the scale. A larger absolute t value gives stronger evidence against the null claim. The p value estimates how unusual the result is, assuming the null claim is true. A small p value supports rejection at the selected alpha level.

The confidence interval gives practical context. If a two sided interval misses the null value, the matching two sided test is usually significant. The interval width depends on sample variation, sample size, and confidence level. More data usually narrows the interval. More confidence usually widens it.

Why Details Matter

A one sample t method assumes independent observations. It also works best with roughly normal data. Large samples reduce sensitivity to mild skew. Very small samples need careful review. Outliers can change the mean, standard deviation, interval, and p value.

For reporting, include the sample mean, standard deviation, degrees of freedom, t statistic, p value, confidence level, and interval bounds. Also state the alternative hypothesis. This makes the conclusion clear and repeatable.

Useful Reporting Workflow

Start with raw data when possible. Check the calculated descriptive statistics. Review the standard error. Compare the p value with alpha. Then read the interval. Use the export buttons to save the evidence. CSV is helpful for spreadsheets. PDF is helpful for sharing a short report.

This calculator gives advanced output, but judgment remains important. Statistics supports decisions. It does not replace study design, sampling quality, or subject knowledge. Use results with context, caution, and clear written assumptions every time.

FAQs