Red Shift

One of the most passed on misconceptions in Physics teaching concerns the red shift of electromagnetic waves. Students in science classes are taught about the Doppler effect of sound waves. If a rapidly moving car moves away from us the sound waves that we hear appear to be stretched out and we hear a lower pitch. Students are then taught that when a very rapidly moving luminous object moves away from us the light waves are stretched out and in this case the effect is known as a red shift. However, is the reverse true? If we observe a red shift does it mean that the object making the light waves must be moving away from us?