The statement is false.
The escape velocity from a planet is given by the expression [tex]\sqrt{\frac{2GM}{r}}[/tex] where G is the gravitational constant, M is the mass of object and r is the distance to center of the planet to the object.
We also have [tex]GM = gr^2[/tex], where g is acceleration due to gravity .
On substitution we will get
Escape velocity = [tex]\sqrt{\frac{2gr^2}{r} } =\sqrt{2gr}[/tex]
The escape velocity does not depend upon mass of object.
So the escape velocity is same for larger and smaller rockets.
