Question

Use the table below to answer the following questions.

Source	df	SS	MS	p-value
A	1	1.36	1.360	0.266
B	1	0.622	0.622	0.451
AB	1	22.405	22.405	0.000
Error	132	143.948	1.091	x
Total	135	168.335	x	x

a) How many levels (a) are there for factor A?

b) How many levels (b) are there for factor B?

1) Test for treatment effect $LaTeX: \alpha=0.05$ α=0.05

H0: No treatment effect vs Ha: There is some treatment effect

F=

Reject H0 if F>  (use F0.05,3,120 as the critical value)

Conclusion:  (type reject or fail to reject)

Interpretation: There  sufficient evidence to support that there is a treatment effect. (type is or is not)

Is it appropriate to conduct for an interaction effect?  (type yes or no)

2) Test for interaction effect $LaTeX: \alpha=0.05$ α=0.05

H0: No AB interaction vs Ha: Factors A and B interact

p-value=

Reject H0 if p-value< $LaTeX: \alpha$ α

Conclusion:    H0 (type reject or fail to reject)

Interpretation: There  sufficient evidence to support that there is an interaction effect. (type is or is not)

Should the factor effect tests be conducted?  (type yes or no)

Answer 1

a)

levels (a) are there for factor A =df(A)+1 =1+1 =2

b)  levels (b) are there for factor B =df(B)+ 1=1+1 =2

1)F_A= MSA/MSE =1.36/1.091=1.25 ; F_B =0.622/1.091 =0.57

Reject H0 if F> 3.91

Conclusion:   fail to reject

There  is not sufficient evidence to support that there is a treatment effect.

No

2)

p-value= 0.0000

Reject H0 if p-value<0.05

Conclusion:  reject

There is sufficient evidence to support that there is an interaction effect

Should the factor effect tests be conducted : Yes