T-Statistic Calculator
Calculate the t-statistic for a one-sample t-test comparing a sample mean to a hypothesized population mean.
T-Statistic
2.000000
T-Statistic vs Sample Mean
Formule
## 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.
Exemple Résolu
Sample mean = 52, hypothesized mean = 50, sample SD = 5, n = 25.
- 01SE = 5 / sqrt(25) = 5 / 5 = 1
- 02t = (52 - 50) / 1 = 2
- 03df = 25 - 1 = 24
- 04Compare t = 2 to the t-distribution with 24 df
- 05Critical value at alpha=0.05 (two-tailed): approximately 2.064
- 06Since |t| = 2 < 2.064, the result is not quite significant at 5% (two-tailed).
Questions Fréquentes
When should I use t instead of z?
Use the t-statistic when the population standard deviation is unknown and you estimate it from the sample. With large samples (n > 30), the t and z distributions are nearly identical.
What does degrees of freedom mean?
Degrees of freedom (df = n-1) accounts for the fact that estimating the mean uses up one piece of information. More df means the t-distribution is closer to the normal distribution.
Is a larger absolute t-value better?
A larger |t| means the sample mean is further from the hypothesized mean relative to sampling variability, providing stronger evidence against the null hypothesis.
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