For an analysis of variance comparing four treatment means with a separate sample of n = 8 participants in each treatment, the f-ratio will have df = 3, 31.

False

Explanation:

To get the F-ratio, we make use of the degree of freedom of sum of square treatment and sum of square error.

D.F for SStreatment = t - 1 = (4-1) = 3

D.F for SSerror = N - t = (32-4) = 28

Where t is the number of treatment, N is the total number of samples (8×4=32)

Thus, the right degree of freedom for the F-ratio is DF= 3, 28.

according to classical republican political theory, which democratic republics would function best?

a.   small republics, with people who had similar interests

b.   large republics, with people who had competing interests

c.   republics made up entirely of landowners

d.   republics made up entirely of servants