There is also another 1900 census with the name "Luck Hick" At the time, Luke is 29 and they say he is born Nov 1870. They are living in Civil District 6, Marion, Tennessee.
Rachel is 19 and Maudie, (which they have as Mandie) is 6/12.
I do believe that this is the correct census.
On the same page is an Anderson Hicks who is married to a Nancy. The birth years for their children are fairly close and it skips a few years, which could allow Luke to be born in. However, I can not prove this is his dad.