LaTeX
t=\frac{\bar x-\mu_0}{s/\sqrt n}Variables
- x̄: sample mean
- μ0: hypothesized mean
- s: sample standard deviation
- n: sample size
How to use this formula
Standardizes a sample mean when population standard deviation is unknown.
Important notes
- The classic test assumes independent observations and approximate normality.
- Degrees of freedom are n−1.
Quick example
Compare the computed t with a t distribution having n−1 degrees of freedom.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The classic test assumes independent observations and approximate normality.
- For the One-Sample t Statistic, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For a real-valued result, each even-root radicand must be nonnegative unless complex values are intended.
- For the One-Sample t Statistic, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
Compare the computed t with a t distribution having n−1 degrees of freedom.
Common mistakes
- When copying One-Sample t Statistic, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the One-Sample t Statistic, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use One-Sample t Statistic in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
t=\frac{\bar x-\mu_0}{s/\sqrt n}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the One-Sample t Statistic used for?
Standardizes a sample mean when population standard deviation is unknown.
Can I copy this formula as LaTeX?
Yes. Copy t=\frac{\bar x-\mu_0}{s/\sqrt n} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.