The Huntington Chemical Co. has been accused of dumping improperly treated waste in a local trout lake, and litigation may be imminent. The central allegation is that the trout population has been severely reduced by the company's dumping practices. The company counters with the claim that there still remain at least 100,000 trout in the lake, and this being a substantial number for a lake of its size, they are innocent of all charges. In order to investigate the size of the trout population, 500 trout are captured, tagged, and then returned to the lake. After the fish have redistributed themselves in the lake, 500 fish are captured, and the number of tagged fish are observed. Letting \(\bar{X}\) represent the proportion of tagged fish, can a size \(\leq .10\) test of the company's claim be defined? Would an outcome of \(\bar{x}=.14\) support or contradict the company's claim?