If the students moved the ends of the rope up and down the same distance but faster, the most accurate description of the changes in the wave characteristics would be:
The frequency would increase and the wavelength would decrease, but the amplitude would be unchanged.
As they move their hands faster, they create more cycles of the wave in a given period of time, which increases the frequency. Since the speed of the wave remains constant, a higher frequency means that the wavelength must decrease. The amplitude, which is the height of the waves, will remain unchanged because they are still moving the ends of the rope the same distance up and down.