I took a quick look at the Rhode Island directories database at Ancestry and found entries for James I Hickman (Mary Ann) including some dated from 1929 to 1931 in Provindence. In the Providence City, 1932 directory it had the following entry:
Hickman, Jas I (Mary Ann) died 4 June 1931
Hickman, Mary Ann wid Jas J h 5 Calderwood road
The initial for James in the entry for Mary Ann would appear to be a typographical error in the directory. That address is the same one that was listed for Jas I Hickman in the directory entries for other years that I looked at as well as being the same address they were at on the 1920 census.
I found James and Mary Ann on the 1930 census (there surname was mistranscribed as Heckman at Ancestry):
5 Calderwood Road, Providence City, Providence, RI - Ward 1, Enumeration District: 131, page 1A
James I. Hickman, head, 54 (there is an age listed that is crossed out and 54 is printed above it), age at first marriage 28, born England, parents born England, immigrated 1902, alien, caretaker for private family
Mary A Hickman, wife, 64, age at first marriage 35, born Irish Free State, parents born Irish Free State, immigrated 1902, alien
Jacquie