One-Sample t-Test
Enter your sample statistics (mean, standard deviation, size), the hypothesized population mean μ₀, the significance level α and pick a one- or two-tailed alternative. The calculator computes the t statistic, the standard error, the degrees of freedom, the critical values and the p-value, then concludes whether to reject H₀.
Frequently asked questions
When do I use a t-test instead of a z-test?
Use a t-test when the population standard deviation is unknown and you estimate it from the sample. For large n (≈ 30+) the t and z results converge.
What does 'two-tailed' mean?
Two-tailed tests reject H₀ when the sample mean is significantly larger OR smaller than μ₀. One-tailed tests look only in one direction; they give a smaller p-value for the right side at the cost of missing deviations on the other.
How is the p-value computed?
From the Student-t distribution with df = n − 1, using a regularized incomplete beta function for accuracy across all degrees of freedom.