All 13 people aboard a New Zealand skydiving plane whose engine apparently failed Wednesday managed to leap out in parachutes moments before the plane plunged into a lake, the authorities said. Roy Clements, the chief executive of Skydive Taupo, the plane’s operator, said the six passengers were all foreign tourists who had each been assigned an instructor for a tandem dive. But soon after the plane took off, something went wrong at about 2,000 feet. “The plane just made a big bang, and then it stopped,” Mr. Clements said. “The pilot told them to get out. He didn’t have to tell them twice.” Mr. Clements said that the instructors had already been wearing parachutes, but that they had needed to clip on their passengers’ harnesses hastily before leaping from the plane. He said that the pilot had also been wearing a parachute, which is standard in skydiving operations, and that he leapt only after ensuring everybody else was safely off the plane. No one was badly hurt, the police said.