  Artin's Conjecture on Primitive Roots states that a non-square nonunit
integer $a$ is a primitive root modulo $p$ for the positive proportion of $p$.
This conjecture remains open, but on average, there are many results due to P.
J. Stephens. There is a natural generalization of the conjecture for composite
moduli. We can consider $a$ as the primitive root modulo,
$(\mathbb{Z}/n\mathbb{Z})^{*}$ if $a$ is an element of the maximal exponent in
the group. The behavior is more complex for composite moduli, and the
corresponding average results are provided by S. Li and C. Pomerance, and
recently by the author. P. J. Stephens included the second moment results in
his work, but for composite moduli, there were no such results previously. We
prove that the corresponding second moment results in this case.
