TAOCP 3.3.1 Exercise 1
Equation (5) arises from the dice-throwing experiment with eleven categories, namely the possible sums $2,3,\ldots,12$.
Section 3.3.1: General Test Procedures for Studying Random Data
Exercise 1. [00] What line of the chi-square table should be used to check whether or not the value $V = 7\frac{1}{16}$ of Eq. (5) is improbably high?
Verified: yes
Solve time: 1m03s
Equation (5) arises from the dice-throwing experiment with eleven categories, namely the possible sums $2,3,\ldots,12$. Therefore $k=11$.
By the rule stated in Section 3.3.1, the chi-square table should be used with $\nu=k-1$ degrees of freedom. Hence
$\nu = 11-1 = 10.$
Therefore the correct line of Table 1 is the row for $\nu=10$ degrees of freedom.
$\boxed{\nu=10}$