t-Test Calculator

Compute one-sample t statistic from sample mean, population mean, and sample SD.

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What This Calculator Does

Compute one-sample t statistic from sample mean, population mean, and sample SD.

It combines Sample Mean, Population Mean, Sample SD, Sample Size to estimate t Statistic, Degrees of Freedom.

Formula & Method

Core equations: One-sample t-stat:

t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}

Notation used in the formulas: $R$ = t Statistic; $x_{1}$ = Sample Mean; $x_{2}$ = Population Mean; $x_{3}$ = Sample SD; $x_{4}$ = Sample Size.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Reference Book

Introduction to Mathematical Statistics

Global Edition

Robert V. Hogg, Joseph McKean, and Allen T. Craig · Pearson

A standard reference for probability distributions, estimation, hypothesis testing, regression, and ANOVA.

View Book

Inputs Used

Sample Mean: Used directly in the calculation.
Population Mean: Used directly in the calculation.
Sample SD: Used directly in the calculation.
Sample Size: Used directly in the calculation.

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