Using a t-distribution table can be a trick. The table is arranged with degrees of freedom across the rows and probabilities down the columns; the t values appear at the intersections of rows and columns.
Given the t-distribution's symmetry, the table only presents probabilities greater than 0.5, and then only at selected probabilities. If t has a probability p of being at most v > 0, then it has a probability 1 - p of being at most -v.
In the example, with 9 degrees of freedom, the t value 2.11 (flipped from negative to positive for the table) falls between the table values 1.83 and 2.26 with probabilities 0.95 and 0.975 respectively. Setting up the linear interpolation gives
Solving for p, the unknown probability, gives
Flipping back to original negative t value gives the probability 1 - 0.966 = 0.034.
This page last modified on 2 March 2005.