Suppose we ask 50 men and 150 women whether they are early risers, late risers, or risers with no preference. The data are given in the following table.

$\begin{array}{lcccc} & \text { Early risers } & \text { Late risers } & \text { No preference } & \text { Totals } \\ \text { Men } & 17 & 22 & 11 & 50 \\ \text { Women } & 43 & 78 & 29 & 150 \\ \text { Totals } & 60 & 100 & 40 & 200\end{array}$

Derive carefully a (generalized) likelihood ratio test of independence of classification. What is the result of applying this test at the $0.01$ level?

$\left[\begin{array}{lccccc}\text { Distribution } & \chi_{1}^{2} & \chi_{2}^{2} & \chi_{3}^{2} & \chi_{5}^{2} & \chi_{6}^{2} \\ 99 \% \text { percentile } & 6.63 & 9.21 & 11.34 & 15.09 & 16.81\end{array}\right]$