Got a picture?
1" sounds way under sized for a stringer.
A stringer again a wall needs to have a 2 X 4 behind it at the bottom of it so the skirt board and sheetrock can slip in behind the stringer so there no cutting around the riser and tread area needed.
The bottoms of the stringers need to be cut into the under side so a piece of pressure treated 2X can be used to hold the stringers in line and give you a place to fasten the whole thing to the floor.
1" sounds way under sized for a stringer.
A stringer again a wall needs to have a 2 X 4 behind it at the bottom of it so the skirt board and sheetrock can slip in behind the stringer so there no cutting around the riser and tread area needed.
The bottoms of the stringers need to be cut into the under side so a piece of pressure treated 2X can be used to hold the stringers in line and give you a place to fasten the whole thing to the floor.