Is turning off the a/c unit more efficient than raising or lowering the thermostat. Whenever the outdoor temperature cools below 70 degrees, my house mate shuts off the whole air conditioning unit.

Is turning off the a/c unit more efficient than raising or lowering the thermostat. Whenever the outdoor temperature cools below 70 degrees, my house mate shuts off the whole air conditioning unit.
The answer to that question is simple. Your house mate is correct !
Point 1 : if you do not use the cooling/heating mode do not leave the fan running. It is much cheaper the run a normal table fan instead, if you want air movement.
Point 2 : one to two steps lower on heating (less heat) or one or two steps higher on cooling (less cool) also saves you a fortune. That also goes for your central heating system.
:)

Your housemate turning off the unit is okay. If you wish to adjust the thermostat that is okay also. The totally turning off the unit is the choice that actually will save you money in the end. If you are not home during the daytime and you wish to adjust the thermostat so that the daytime temp is at say 79 or 80 degrees that's okay as when you come home from work you can adjust the temp to a lower say 74 or 75 degrees. In the summertime I raise the temp during the day to about 80 when I am not home.