Enter the sample mean, hypothesised population mean, sample standard deviation and sample size to compute the one-sample t statistic (xbar - mu)/(s/sqrt(n)) and its degrees of freedom.
|t| 越大，拒绝原假设的证据越强。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| One-sample t statistic | t = (xbar - mu) / (s / sqrt(n)) | Student (1908), The probable error of a mean, Biometrika 6(1) |
| Degrees of freedom | df = n - 1 | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.2 |
| Decision rule | Reject H0 when |t| > t(1 - alpha/2, n - 1) for a two-sided test | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.2 |
| Normality assumption | Small samples require near-normal populations; large samples rely on the CLT | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.2 |