Finally. I have found the Baker Family in the 1930 Census. I first searched for Clarence Baker in Familysearch.org and low and behold, the family popped up. There they were: Clarence Lee Baker, Hazel M. Baker and Clarence M. Baker. All the birthdates looked good, as did parent's birth places. FINALLY.
But I searched again in ancestry and did not come up with them. It's not a difficult name. All other documents tell me they've been in the U.S. for a while. But nothing. I've previously searched for Clarence and Hazel in Gary, IN to no avail.
Using the information from familysearch, I looked up the pages in the U.S. 1930 Census manually.
I found them under Barker, Clarence, Habel and Clarence. The annotator must have been drunk that day or something because it's clearly Baker. Oh well. Here it is, finally: