Question

The college of business was interested in comparing the interaction of academic status and class time on class attendance. Three different classes were sampled for each cell in the table. The means for each cell follow.

Academic status	8:00 am Class	9:30 am Class	11:00 am Class
Freshman	25	30	25
Sophomore	30	32	30
Junior	32	35	40
Senior	32	40	39
Graduate students	35	33	30

What are the interaction degrees of freedom?

What are the block and treatment degrees of freedom?

What is the treatment variable?

What is the critical F statistic for testing the hypothesis of equal treatment means at the 0.05 significance level?

Answer 1

a)

Interaction degree of freedom will be

Level of academic status=x=5

Level of class time =y=3

Degree of freedom for interaction will be (x-1)(y-1)=(5-1)(3-1)=4*2=8

So  interaction degrees of freedom are eight

b)

Block degree of freedom is given as (No of blocks-1)=(3-1)=2

Treatment degree of freedom is given as=(5-1)=4

c)

Treatment variable is the explanatory or independent variable which is manipulated by experimenter

Each factor has two or more levels different values of factor

Combination of factor levels are called treatment

here the treatment variable is academic status

d)

critical F statistic for testing the hypothesis of equal treatment means at the 0.05 significance level will be

Let us first find the degree of freedom for numerator and denominator

D.F for numerator=(3-1)=2

Degree of freedom for denominator will be D.F=(15-3)=12

and alpha level is given as 0.05

As per F table using degree of freedom

F critical value is given as 3.84