The President's Mystery is a 1936 American film directed by Phil Rosen.
I Killed That Man is a 1941 American film directed by Phil Rosen that was a remake of his 1933 film "The Devil's Mate".
 It starred Ricardo Cortez and was produced by the King Brothers.
Beggars in Ermine is a 1934 American film directed by Phil Rosen.
Paul Bogart (November 21, 1919 – April 15, 2012) was an American television and film director and producer.
Born to Gamble (1935) is an American film directed by Phil Rosen and released by Republic Pictures.
Phil Rosen (May 8, 1888 – October 22, 1951) was an American film director and cinematographer.
 He directed 142 films between 1915 and 1949.
The Scarlet Clue is a 1945 American film directed by Phil Rosen.
Road to Happiness is a 1942 American film directed by Phil Rosen.
Roar of the Press is a 1941 American film directed by Phil Rosen.
Paper Bullets is a 1941 American film directed by Phil Rosen and starring Joan Woodbury.
 It was the first film produced by the King Brothers, launching their career.

Question: Are Phil Rosen and Paul Bogart American film directors?
Answer: yes