e-Statistics > 4480-5480 Probability and Statistics II

t-Distribution

The t distribution is symmetric but comparatively flatter (see the solid line in the graph below) than the standard normal distribution (the dashed line below). The shape of particular t-distribution is determined by the degrees of freedom (df) = .

We can calculate the critical region corresponding to the level $ \alpha$.

Level (p-value) $ \alpha =$
Right-tailed region $ T > t_{\alpha,df} =$
Two-sided region $ \vert T\vert > t_{\alpha/2,df} =$
Left-tailed region $ T < -t_{\alpha,df} =$

t-distribution table contains the selected critical values in a form of table.

Conversely when the statistic $ T =$ is given, we can find the corresponding $ \alpha$ so that the value $ T$ belongs to the critical region, and call it p-value.