Question

Researchers at a state agricultural station conduct a series of experiments to investigate the feeding habits of baby chickens. Chicks were deprived of food until their guts were empty and then were allowed to feed for 6 hours on a diet of corn or mixed grains. For each feeding trial, the change in the weight of the chicks after 6 hours was recorded as a percentage of the bird's initial weight. The digestive efficiency (measured as a percentage) for each chick was also recorded. The data is given in the table below.

Type of feed	corn	corn	corn	corn	corn	mixed	mixed	mixed	mixed	mixed
Digestion Efficiency (%) (xx)	2	2	0	1.5	1.5	41	57.5	62.5	64.5	43.5
Weight Change (%) (yy)	0	3.5	-0.5	-5	-0.5	10.5	12.5	14.5	7.5	10

(a) Conduct a test to determine whether weight change, yy, is linearly related to digestion efficiency, xx.
State the test statistic t=t=

(b) Using α=0.05α=0.05, we conclude:

A. There is not sufficient evidence of a linear relationship.
B. There is sufficient evidence of a linear relationship between digestive efficiency and weight gain.

(c) Repeat part (a), but exclude the data from the trials that used the mixed grains feed.
State the test statistic tcornonly=tcornonly=

(d) Again, using α=0.05α=0.05, we conclude:

A. There is not sufficient evidence of a linear relationship for the corn only group.
B. For the corn only group, there is sufficient evidence of a linear relationship between digestive efficiency and weight gain.

Answer 1

SSE =Syy-(Sxy)2/Sxx=

78.737

	s2 =SSE/(n-2)=	9.8421
std error σ              =	=se =√s2=	3.1372

null hypothesis: Ho:               β1		=	0
Alternate Hypothesis: Ha: β1		≠	0
0.05 level,two tail test and n-2= df, critical t=			2.306

estimated std error of slope =se(β1) =s/√Sxx=			0.0366
test stat t =	(bo-β1)/se(β1)=	=	5.6698
p value:		=	0.0005

since p value <0.05 , we reject null and conclude that  

B. There is sufficient evidence of a linear relationship between digestive efficiency and weight gain.

c)

test stat t =	(bo-β1)/se(β1)=	=	0.4031
p value:		=	0.7139

d)

A. There is not sufficient evidence of a linear relationship for the corn only group.