AP Stats Degrees of Freedom

Question

Randall is conducting a test on bacteria on slices of cheese. He uses 10 slices of cheese to compare two strains of bacteria. He applies one strain to the left side of the cheese and one strain to the right side. He flips a coin to decide which strain goes on the right side of the cheese. The bacteria holes that appear on each side are counted and he records them in a table.

Cheese Number of Holes for Strain 1 Number of Holes for Strain 2

1	25	19
2	21	15
3	13	14
4	13	12
5	14	10
6	12	9
7	11	5
8	11	5
9	8	4
10	5	4

If Randall is to perform an appropriate t-test to determine if there is a mean difference between the mean number of holes per slice of cheese produced by the two strains, how many degrees of freedom should he use?

Answer 1

Since he is applying the two treatments to the same slice of cheese, a paired t-test would be appropriate here. The number of degrees of freedom would be the number of slices of cheese (10) - 1 = 9.