## 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 .

Level (p-value) | |

Right-tailed region | |

Two-sided region | |

Left-tailed region |

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

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