Calculadora de Teste t (uma amostra)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
t = (x̄ − μ₀) / (s/√n)
About this calculator
The One-Sample t-Test Calculator is a statistical tool that computes the t-value and degrees of freedom from the sample mean, sample standard deviation, and sample size. The one-sample t-test is used to determine if the mean of a population differs significantly from a reference value (μ₀). The formula is t = (x̄ − μ₀) / (s/√n), where x̄ is the sample mean, s is the sample standard deviation, and n is the sample size.
The operation is simple: input the sample mean, sample standard deviation, sample size, and the hypothesized value μ₀. The calculator returns the t-value and degrees of freedom (n-1). These values can be compared with the Student's t-distribution table to determine statistical significance. The test assumes approximately normal and independent data.
Use this calculator in scenarios such as: checking if the average height of a class differs from the national average, testing if the mean loading time of a website exceeds an acceptable limit, or analyzing if the average student score differs from a set standard. It is useful in scientific research, quality control, and educational analysis.
Important precautions: the t-test is sensitive to outliers and data normality. For small samples (n < 30), check normality. If data are highly skewed or have outliers, consider a nonparametric test. Also, the sample standard deviation should be calculated with n-1 in the denominator (Bessel's correction).
Frequently asked questions
What does the calculated t-value mean?
The t-value indicates how many standard deviations the sample mean is from the hypothesized value μ₀. The larger the absolute t-value, the stronger the evidence against the null hypothesis.
How do I know if the result is significant?
Compare the t-value with the critical value from the Student's t-distribution table for the degrees of freedom (n-1) and the desired significance level (e.g., 0.05). If |t| > critical value, reject the null hypothesis.
Can I use this calculator for small samples?
Yes, but for samples with n < 30, it is important that the data are approximately normal. Otherwise, the test may not be reliable.
What are degrees of freedom?
Degrees of freedom (df) are the number of independent values that can vary in the analysis. In the one-sample t-test, df = n - 1, where n is the sample size.
What is the difference between one-tailed and two-tailed t-tests?
The two-tailed test checks if the mean is different from μ₀ (either higher or lower). The one-tailed test checks if the mean is greater than or less than μ₀. This calculator provides the t-value for both cases.