Question

Suppose a friend plans a study to determine the efficacy of a new antibiotic in dairy cattle. The treatments will be a placebo (control) and an antibiotic injection. Forty cows in 4 separate pens of 10 cows are used. Cows are first assigned at random to each of the 4 pens. Within each pen, 5 cows are assigned at random to the placebo and 5 cows are assigned to the antibiotic injection. Use this information to answer questions  identified as study 1.

How many degrees of freedom for error will she have to evaluate differences between cows that received antibiotic compared to those that did not in study 1?

a. 2

b. 3

c. 32

d. 33

Answer 1

Answer: c) 32

Explanation:

The degrees of freedom for error = ab(r-1)

                                                      = (4)(2)(5-1)

                                                       = 32