1. Researchers conducted a study of the effects of three drugs on the fat content of theshoulder muscles in Labrador retrievers. They allocated 80 dogs at random to four treatment groups. The dogsin group A were the untreated controls, while groups B, C, and D received one of the three new heartwormmedications in their diets. Five dogs randomly selected from each of the four groups received varying lengthsoftreatment from4monthsto2years.Thepercentagefatcontentoftheshoulder muscleswasdetermined.Thefollowingis adescription ofthe variablesinthe data file:

Column	Nameof variable	DescriptionofVariable
1	Fat	Percentagefat content
2	Treat	Treatment (A=1,B=2,C=3,D=4)
3	Time	Length oftreatment(4, 8, 12, 24)

Usetheinformationbelow toanswerthefollowingquestions:

a) Carry out a test to determine if there is significant evidence of difference in mean percentage fatcontent inthefourtreatmentgroups.

b) Carry out a test (regardless of your results in part (a)) to determine if there is significantevidenceof differencein meanpercentage fatcontentin thethreetreatment groupsB,C, andD.

c) Suppose the researchers conjectured that the new medications caused an increase in fat contentand that this increase accumulated as the medication was continued in the dogs. Define a contrast that is ameasure of the linear relationship between the lengths oftreatment (time) and the mean of fat content.Carryouta testaboutthe conjecture. Interpretyour conclusion.

d) Another way to quantify the strength of the linear relationship between the lengths of treatment(time) and the mean of fat contentis to fit the regression model m_Y=b₀+b₁*Time. Fit the regressionmodeland carryouta testforH0:b₁=0versusH1:b₁0.Interpretyourconclusion.

e) Arep-valuesinparts(c)and(d) thesame? Shouldtheybe?Explain youridea.

Question #3Output:

	N	Mean	Std.Deviation	Std.Error
Treatment
A	20	2.4615	.27808	.06218
B	20	2.6940	.40883	.09142
C	20	2.6055	.40889	.09143
D	20	2.6980	.31961	.07147
Total	80	2.6148	.36454	.04076

ANOVATable (ComparingallFourGroups):

ANOVA

Fat

	SumofSquares	df	MeanSquare	F	Sig.
BetweenGroups	.736	3	.245	1.909	.135
WithinGroups	9.763	76	.128
Total	10.498	79

ANOVATable(IgnoringTreatmentstreatinggroups B,C, andDasthesame):

ANOVA

Fat

	SumofSquares	df	MeanSquare	F	Sig.
BetweenGroups	.626	1	.626	4.948	.029
WithinGroups	9.872	78	.127
Total	10.498	79

ANOVA Tableand EstimatedParameters for Regression Model:m_Y=b₀+b₁*Time

Model		SumofSquares	df	MeanSquare	F	Sig.
1	Regression	3.206
	Residual	7.292
	Total	10.498

aPredictors:(Constant),TimebDependentVariable:Fat

Coefficients^a

Model	UnstandardizedCoefficients	StandardizedCoefficients	t	Sig.
B	Std.Error	Beta
1 (Constant) Time	2.294 .027	.065 .005	.553

a.DependentVariable:Fat

Linearcontrast: