N1031T, a DC-9-31, was in a descent for landing at Jamaica, NY. The captain reported he heard a noise that he thought was a failing cabin door pressure seal and advised the copilot. The copilot indicated he thought the noise was the sound of a jet engine. Between 1453 and 1455, the crew of N1031T observed a Grumman F-14A, USN, maneuver above and around their aircraft. N1031T was on a heading of 275 degrees and USN was on a heading of 250 degrees. N1031T turned approximately 15 degrees right and USN banked right and disappeared from view. No other evasive action was taken by N1031T and it landed at JFK Airport without further incident. USN landed at Calverton and reported he observed no conflicting traffic. New York ARTCC and New York TRACON recorded data disclosed between 1454:00 and 1454:35 minimum horizontal separation of 0.7 nautical miles occurred at 13,200 feet and minimum vertical separation of 200 feet occurred at 12,900 feet.