It shall thereupon be the duty of the board of the school district or districts with which such statement has been filed, to apportion for attendance to the said model school or training department, a sufficient number of pupils from the public schools under the supervision of said board as will furnish to such regional university the number of pupils required in order to maintain such facility: PROVIDED, That the president of said regional university may refuse to accept any such pupil as in his or her judgment would tend to reduce the efficiency of said model school or training department.