T-Statistic Calculator — 公式
## How to Calculate the T-Statistic
### Formula
**t = (x_bar - mu) / (s / sqrt(n))**
The t-statistic measures how many standard errors the sample mean is from the hypothesized population mean. It follows a t-distribution with n-1 degrees of freedom. Use the t-test instead of the z-test when the population standard deviation is unknown and estimated by the sample SD.
### Formula
**t = (x_bar - mu) / (s / sqrt(n))**
The t-statistic measures how many standard errors the sample mean is from the hypothesized population mean. It follows a t-distribution with n-1 degrees of freedom. Use the t-test instead of the z-test when the population standard deviation is unknown and estimated by the sample SD.
计算示例
Sample mean = 52, hypothesized mean = 50, sample SD = 5, n = 25.
- SE = 5 / sqrt(25) = 5 / 5 = 1
- t = (52 - 50) / 1 = 2
- df = 25 - 1 = 24
- Compare t = 2 to the t-distribution with 24 df
- Critical value at alpha=0.05 (two-tailed): approximately 2.064
- Since |t| = 2 < 2.064, the result is not quite significant at 5% (two-tailed).