  Csikv\'{a}ri constructed a poset on trees to prove that several graph
functions attain extreme values at the star and the path among the trees on a
fixed number of vertices. Reiner and Smith proved that the Tutte polynomials
$T(1,y)$ of cones over trees, which are the graphs obtained by attaching a cone
vertex to a tree, have the described extreme behavior. They further conjectured
that the result can be strengthened in terms of Csikv\'{a}ri's poset. We solve
this conjecture affirmatively.
