The correct answer is false.
It is false that in the wake of the Seven Years' War, there was no longer any need for a large military presence in the American colonies, so the British government withdrew its troops to save money and appease suspicious colonists.
What started as the French and Indian War in 1754 due to territorial dominions between the French and the English, ended up in the Seven Year's War, an international conflict that included Great Britain, Spain, France, Prussia, Austria, Russia, Sweden, and France. Of course, a heavy military presence was needed in the American territories and the British Royal Navy played a major role in the English victory.