ok, lets go back to the top
what is the voltage and amperage of the load your going to be switching on and off?
you need to know that so you can choose the correct part, if its low voltage and amperage (~ <500ma) your 2222 nPn transistor should do fine
If it is mains (120-240vac) and switching a 4 amp motor then were in a whole new world, but the basic's of operation are the same
arduino (or even the sensor in this case) toggles a ping "high", that voltage (after passing tru current limiting / safety stuff) connects to a switching device, which could be
FET (big transistor)
or SSR (solid state relay, which is not really a relay)
which opens and closes the switch for the other circuit