With the given information you can find the initial and final mechanical energies. Then we can verify the conservation of it.
1) Initially the ball is at rest 1 m over the ground, then its mechanical energy is only potential energy = m*g*h = 2kg * 9.8m/s^2 * 1m = 19.6 joule
2) When the ball is above to hit the ground, its mechanical energy is only kinetic energy = [1/2]m*v^2 = [1/2]2kg*(4.4m/s)^2 = 19.4 joule
Those results, taken into account that the measures have some errors (for example the exact velocity of the ball when it reaches de floor is quite difficult to measure) confirm the conservation of the energy.
Then, the answer is the option B. The mechanical energy is conserved
