Karl,
Please tell me what the "11" means in the "11/2. OH, never mind You meant to write 1 1/2 x 7.
There is no written spec for your type of construction, but through the years we have learned you can indeed install tiles over that framing. (You're on the left coast right?)
Assuming everything is in good shape and the 2x8 decking (2x8's measure 1 1/2 x 7 1/4") are not cupped, you need to install min. 1/2" (prefer thicker), underlayment grade plywood fastened only to the decking. Then thinset your favorite 1/4" CBU, screwed or nailed, seams taped, or you can substitute Ditra and go premium.

Do NOT glue the new underlayment to your subfloor, only screw it with fasteners just long enough to go through the sub. So, for 1/2" ply 2" screws would be perfect. Do not use cheap drywall screws.
Jaz