Question

When a virus is placed on a tobacco leaf, small lesions appear on the leaf. To compare the mean number of lesions produced by two different strains of virus, one strain is applied to half of each of 8 tobacco leaves, and the other strain is applied to the other half of each leaf. The strain that goes on the right half of the leaf is decided by a coin flip. The lesions that appear on each half are then counted. The data are given below:

Leaf Strian 1 Strain 2
1 31 18
2 20 17
3 18 14
4 17 11
5 9 10
6 8 7
7 10 5
8 7 6
What is the number of degrees of freedom associated with the apropriate t-test for testing to see if there is a difference between the mean number of lesions per leaf produced by the two strains?
a. 7.
b. 8.
c. 11.
d. 14.
e, 16.

Answer 1

Answer: a. 7

Explanation: Degrees of Freedom is the number of values "allowed" to vary. For example:

In the experiment above, the sample has 8 tobacco leaves. Two strains will be applied to each leaf. The decision of which strain goes to the right or left is random. Each strain have 7 possible leaves it can be applied, because, for the last, the eight leaf, there is no choice.

Therefore, the degrees of freedom for this experiment is 7.

It can also be calculated as

df = n - 1

df = 8 - 1

df = 7