Answer: 8
Explanation:
The degree of freedom for t-distribution of testing the differnce between the two population mean is given by :-

, where
= Size of first sample.
= Size of second sample.
As per given ,
Veterinarian selects five horses that are known to have enteroliths and compares the number of flakes of alfalfa they have eaten over a month with the number of flakes eaten by five horses free of enteroliths.
i.e.
and

Now , If she calculates a two-sample confidence interval by hand for the difference in the mean number of flakes fed to horses with and without enteroliths the degrees of freedom she should use are

Hence, the correct answer is 8.