(a) No nursing home which is licensed by the department of public health to provide nursing care may operate except under the supervision of a nursing home administrator duly licensed by the board.
(b) No person shall be admitted to or permitted to take an examination for license as a nursing home administrator unless he shall have first submitted evidence satisfactory to the board, (1) that he is over eighteen years of age, (2) that he is a citizen of the United States, (3) that he is of good moral character, (4) that he is suitable and fit to be licensed and to practice as a nursing home administrator.