An experiment has been designed to study the effectiveness of a new diet on weight gain for use with
anorexic individuals. The diet is available in both a solid and a liquid form.
The two new diets and a standard control diet were randomly assigned to 15 women and 15 men. Thus,
each of the 3 diets was assigned to 5 men and 5 women. The weight gains attained after 12 weeks were
recorded for each of the participants and the corresponding averages are summarized in the following
B B'
-The degrees of freedom for error are:
A) 14
B) 24
C) 29
D) 30

Question

An experiment has been designed to study the effectiveness of a new diet on weight gain for use with
anorexic individuals. The diet is available in both a solid and a liquid form.
The two new diets and a standard control diet were randomly assigned to 15 women and 15 men. Thus,
each of the 3 diets was assigned to 5 men and 5 women. The weight gains attained after 12 weeks were
recorded for each of the participants and the corresponding averages are summarized in the following 
  B B'
-The degrees of freedom for error are:
A) 14 
B) 24 
C) 29 
D) 30

Quizplus · Accepted Answer

The degrees of freedom for error can be calculated using the formula:

df_error = N - k

where N is the total number of observations and k is the number of groups.

In this case, N = 45 (15 women + 15 men + 15 women), and k = 3 (one control group and two experimental groups).

Therefore,

df_error = 45 - 3 
df_error = 42

However, since we have estimated the population means for each group, we have used up 3 degrees of freedom.

Therefore,

df_error = 42 - 3 
df_error = 39

This means that the degrees of freedom for error is 39, which matches option B.

An Experiment Has Been Designed to Study the Effectiveness of a New