T-Test Calculator
Compute the t‑statistic and p‑value for a one‑sample t-test using: $$ t = \frac{\bar{x} – \mu_0}{SD/\sqrt{n}}. $$
* Enter the sample mean (\(\bar{x}\)), hypothesized mean (\(\mu_0\)), sample standard deviation (SD), sample size (\(n\)), and select one‑tailed or two‑tailed test.
Step 1: Enter Test Data
e.g., 100
e.g., 95
e.g., 10
e.g., 30
Select whether the test is one-tailed or two-tailed.
How It Works
1. The T‑score is computed using: $$ t = \frac{\bar{x} – \mu_0}{SD/\sqrt{n}}, $$ where \(\bar{x}\) is the sample mean, \(\mu_0\) is the hypothesized mean, SD is the sample standard deviation, and \( n \) is the sample size.
2. The degrees of freedom for the test are \( n – 1 \).
3. The p‑value is calculated from the t‑distribution. For a two‑tailed test: $$ p = 2\Bigl[1 – F(|t|; n-1)\Bigr], $$ and for a one‑tailed test: $$ p = \begin{cases}1 – F(t; n-1), & t \ge 0,\\ F(t; n-1), & t < 0,\end{cases} $$ where \( F(t; n-1) \) is the cumulative distribution function (CDF) of the t‑distribution.
The calculator uses an approximate method to compute the t‑distribution CDF.
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