讲解 STAT512 Final Exam辅导 C/C++程序

STAT512

Final Exam - Take-Home Part

Due by 11:59pm on Monday, April 27

Instructions: This is the take-home part of the final exam. You are permitted to use your notes, book, calculator, and statistical software in working this exam. However, you are not permitted to receive help from anyone on the exam. Good luck!

1. An animal scientist conducted an experiment to study the effect of water quality on feedlot performance of steer calves. Four water quality treatments were used for the experiment. The water sources were designated as normal (N) and saline (S). The saline water was formulated to approximate the mineral concentrations in some underground water sources utilized in practice for watering livestock. Four combinations of water used in two consecutive 56-day periods of the experiment were N-N, N-S, S-N, and S-S. The feeding trial consisted of the four water treatments with two replicate pens of animals for each treatment in a completely randomized design. The trial was conducted on two separate occasions (two consecutive summers). The water treatments are considered fixed effects and summers are considered random effects. The two factors (water and summer) are crossed. The data are the average daily gains for the 16 pins of steers.

Water

Summer

N-N

N-S

S-N

S-S

2.65

2.53

2.46

2.36

2.56

2.38

2.43

2.50

2.25

2.20

1.95

2.25

2.01

1.98

2.14

2.37

Source: Dr. D. Ray, Department of Animal Sciences, University of Arizona.

a. Set up an analysis of variance table.

Source	SS	df	MS	F	p-value

b. Conduct F test for interaction.

c. If appropriate, conduct F test for Water and F test for Summer. Conduct multiple comparisons for Water if necessary.

d. Assess reasonableness of normality assumption using normal probability plot of residuals and Shapiro Wilk normality test.

e. Assess reasonableness of equal variance assumption using plot of residuals vs fitted (predicted) values.

2. A study was conducted on human subjects to measure the effects of three foods on serum glucose levels. Each of the three foods was randomly assigned to four subjects. The serum glucose was measured for each of the subjects at 15, 30, and 45 minutes after the food was ingested. The data are shown in the table below. Assume Diet and Time are fixed and Subject is random.

Time(minutes)

Diet	Subject	15	30	45
1	1	28	34	32
	2	15	29	27
	3	12	33	28
	4	21	44	39
2	5	22	18	12
	6	23	22	10
	7	18	16	9
	8	25	24	15
3	9	31	30	39
	10	28	27	36
	11	24	26	36
	12	21	26	32

a. What is the name of the experimental design that was used here?

b. Set up an analysis of variance table. Assume that it is appropriate to perform. a split plot analysis of the data and use proc mixed in SAS to perform. the analysis. This is discussed in lecture 24.

Source	SS	df	MS	F	p-value

c. Provide a profile plot that will allow an assessment of the time by diet interaction.

d. Conduct F test for interaction and perform. multiple comparisons using Tukey’s procedure if necessary.

It may not be necessary to do parts e and f.

e. Conduct F test for Diet and perform. multiple comparisons using Tukey’s procedure if necessary.

f. Conduct F test for Time and perform. multiple comparisons using Tukey’s procedure if necessary.

3. Three states were randomly selected to participate in a health awareness study. Each state independently devised a health awareness program. Three cities within each state were randomly selected for participation and five households within each city were randomly selected to evaluate the effectiveness of the program. All members of the selected households were interviewed before and after participation in the program and a composite index was formed for each household measuring the impact of the health awareness program. The data on health awareness follow (the larger the index, the greater the awareness).

What is the name of the experimental design that was used for this experiment?

Construct analysis of variance table using SAS or R.