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Mihsaba›One-Sample T-Test Calculator

One-Sample T-Test Calculator

Calculate the t statistic, degrees of freedom and p-value for a one-sample t-test from sample mean, standard deviation, sample size and hypothesized mean.

The result is mathematical and depends on test assumptions and sampling; it does not replace statistical interpretation of the real context.

How to use

This one-sample t-test compares a sample mean with a hypothesized mean when the population standard deviation is unknown and the sample standard deviation is used instead. It returns t, degrees of freedom, standard error and p-value.

  1. Enter the sample and hypothesized means.
  2. Enter a positive sample standard deviation and integer n≥2.
  3. Choose the alternative-hypothesis tail.
  4. Review t, df, standard error and p-value.

How it is calculated

t=(x̄−μ₀)/(s/√n), with df=n−1

Example

Example: sample mean 52, hypothesized mean 50, sample SD 8 and n=30 gives t≈1.369 with 29 degrees of freedom. The p-value depends on whether the pre-specified alternative is one- or two-tailed.

Important notes

The test assumes independent observations and an appropriate sampling design; for small samples, the shape of the underlying distribution matters more. The calculator cannot validate study design.

Frequently asked questions

t versus z?

t is commonly used when population SD is unknown and estimated from the sample.

What are the degrees of freedom?

For this one-sample test, df=n−1.

Is this a two-sample calculator?

No. This page implements the one-sample t-test.

Does a small p-value prove the alternative?

No. It is evidence within a specified model and assumptions, not absolute proof.