To test the acuity of hearing

A researcher tests the hearing acuity of a group of seniors one week before and one week after an operation. He hopes to show that the seniors hear better after the operation than before. (The higher the score on this test the poorer the hearing). An individual is represented by (X,Y) where X = score before operation and Y = score after operation: (13,14); (11,10); (9, 9); (7,7); (9,2); (6,5); (15,10); (15,10); (10,13); (5,6); (3,2); (18,12).

Can the researcher conclude that the seniors hear better after the operation than before?

I believe that the answer is no, but find the question confusing. Let me know what you think with explanation.

We can use paired t – test for testing.

H0 = scores are equal that is d = 0

H1 = d> 0 (d = x – y)
_
sd = …

Solution to test if there is any improvement in hearing after operation.