  With the success of general conceptual frameworks of statistical physics,
many scholars have tried to apply these concepts to other interdisciplinary
fields, such as socio-politics, economics, biology, medicine, and many more. In
this work, we study the effect of mass media on opinion evolution based on the
nonlinear $q$-voter by means with probability $p$ a voter adopts the mass media
opinion whenever a $q$-sized agent in the population is not in unanimous
agreement. We perform analytical and numerical calculations for some quantities
of macroscopic parameters of the model such as order parameter (representing an
average of public opinion), consensus (relaxation) time, and exit probability,
and obtain the agreement results. We find the power-law relations for some
quantities of the model. (1) The probability threshold $p_t$, i.e a probability
that makes the system reaches a homogeneous state, follows the power-law
relation $p_t \sim q^{\gamma}$ with the $q$-sized agent, where $\gamma = -1.00
\pm 0.01$ is the best fitting parameter. The probability threshold $p_t$ also
eliminates the {coexistence two ordered states} of the model. (2) The
relaxation time (the time needed by the system to reach consensus) $\tau$ with
the population size $N$ is obtained in the form of $\tau \sim N^{\delta}$,
where $\delta$ depends on the probability $p$ and $q$-sized agent. We also
approximate the {separator} point {$r_s$} and the system's scaling parameters
by employing the standard finite-size scaling relation.
