Question

1. Five diets were evaluated for their ability to enable calves to grow, where diet A was the standard diet (used here as reference control) and diets B and C involved supplementation of the standard diet with low and high levels of vitamin B12, respectively. Meanwhile, diets D and E added a mineral supplement to diets B and C, respectively. Thirty four calves were used in this study. A mistake in the feeding of the diets produced an unbalanced distributions of the calves to the diets. The response variable recorded was the number of pounds of weight gained over the duration of the study. The data are provided in the accompanying table.

a) Write down the research question explicitly. Identify the experimental unit for the treatment factor of interest and the observational unit.

b) Specify a factor level effect model for this study. Define all terms in the model and specify any relevant assumptions.

CalfID	Gain	Diet
1	825	A
2	801	A
3	790	A
4	809	A
5	830	A
6	825	A
7	839	A
8	835	A
9	860	A
10	874	D
11	854	D
12	883	D
13	839	D
14	836	D
15	839	D
16	840	D
17	834	D
18	894	D
19	861	E
20	856	E
21	875	E
22	840	E
23	829	B
24	814	B
25	805	B
26	837	C
27	851	C
28	824	C
29	793	C
30	810	C
31	847	C
32	826	C
33	832	C
34	830	C

Answer 1

a. Research under study:-

Here we want to study the effect of various diet on weight of the calf .

Since we have 5 different diets and want to measure the ability of calf to gain weight with such diet we chalk our hypothesis for study

H0: There is no significant difference among the 5 diets (A,B,C,D,E)

v/s

H1: There is a significant difference among the diets

Exeperimental unit= 34calfs

Treatment factor= A , B, C,D, E (Treat each of the 5diets as seperate treatment )

Observation unit= 15units (3 from each treatment / diet recieved)

This is a clear case of Randomized Block Design.

b.

Weight/diet	A	B	C	D	E
w1	825	829	837	874	861
w2	801	814	857	854	856
w3	790	805	824	883	875

The model can be represented as:

where i=1,2,3,4,5 & j=1,2,3.

Can be solved using ANOVA technique

Using assumptions:

• Each group sample is drawn from a normally distributed population.(n>30)
• All populations have a common variance.
• All samples are drawn independently of each other.
• Within each sample, the observations are sampled randomly and independently of each other.
• Factor effects are additive.