  We attempt to construct a Friedmann-Lemaitre-Robertson-Walker(FLRW)
cosmological model in $f(R, T)$ gravity which exhibits a phase transition from
deceleration to acceleration at present. We take $f(R,T) = R + 2 \lambda T$,
$\lambda$ being an arbitrary constant. In our model, the $\lambda$ parameter
develops a negative pressure in the universe whose Equation of state is
parameterized. The present values of model parameters such as density, Hubble,
deceleration, Equation of state, and $\lambda$ are estimated statistically by
using the Chi-Square test. For this, we have used three different types of
observational data sets: the $46$ Hubble parameter data set, the SNeIa $715$
data sets of distance modulus, and the 66 Pantheon data set (the latest
compilation of SNeIa 40 bined plus 26 high red shift apparent magnitude $m_b$
data set in the red shift ranges from $0.014 \leq z \leq 2.26 $). We have
calculated the transitional red shift and time. The estimated results for the
present values of various model parameters are found as per expectations and
surveys. Interestingly, we get the present value of the density $\rho_0$,
$\simeq 1.5 \rho_c $. The critical density is estimated as $\rho_c\simeq 1.88 ~
h_0^2~10^{-29}~gm/cm^3 $ in the literature. The higher value of the present
density is attributed to the presence of some additional energies in the
universe apart from baryon energy. We have examined the behavior of the
pressure in our model. It is negative and produces acceleration in the
universe. Its present value is obtained as $p_0 \simeq - 0.7 \rho_0$.
