This is false because some gases weigh heavier than others. If a gas weighs heavier than another gas, it moves at a slower speed. If the gas moves at a slower speed, its kinetic energy will be less than the lighter gas.
It's false because the avergae kinetic energy of the sample is constant at a constant temperature, but individual molecules, some moving at 20 some moving at 40, do not have the same kinetic energy.