The administrator of a local hospital has told the governing board that 30% of its emergency room patients are not really in need of emergency treatment (i.e., the problems could just as easily have been handled by an appointment with their family physician).
In checking a random sample of 400 emergency room patients, a board member finds that 35% of those treated were not true emergency cases. Using an appropriate hypothesis test and the 0.05 level, evaluate the administrator's statement.