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628 14. Appendix

14.3.3 Percentage Points of the Student’s t Distribution

The Table 14.3.3 provides the lower 100γ% point t v,1–γ for the Student’s t v
distribution for different values of v and γ. See the Figure 14.3.4.

Figure 14.3.4. The Shaded Area Is the Probability γ

Suppose that X has the Student’s t distribution with some appropriate v.
v
Now, consider the following examples:

Remark 14.3.3 The percentage points of the t distribution can be easily
1
found by directly integrating its pdf which happens to be the same as the
Cauchy pdf. Observe that

For example, when γ = .95, one has t 1,.05 = tan (π(.95 - ½)) ≈ 6.3138. In the t
Table 14.3.3, we have t = 6.314.
1,.05