If I let a friend drive the family car and they got a speeding ticket, will that effect my insurance rates?

Good question. Since you were not the person who was driving the vehicle that you own who was ticketed, you would have nothing to worry about with respect to your insurance premiums. However, if you loaned the vehicle to a friend and the friend was in an accident caused by him or her damaging the car, another car and possibly others, your insurance premiums most likely would receive an increase.