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Sma2110:Real Analysis Ii Question Paper
Sma2110:Real Analysis Ii
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
a) Define the following terms as used in the design and analysis of experiment; (i) Experimental error (2 marks) (ii) Blocks (2 marks) (iii)Absolute experiment (2 marks) (iv) Extraneous variables (2 marks) b) Discuss the principles of design of experiment (6 marks) c) A set of data involving four Chinese drugs A,B,C,D tried on 20 dairy cows to influence milk production were as follows:
Drugs Weight of milk produced by each dairy cow
A 55 49 42 21 52
B 61 112 30 89 63
C 42 97 81 95 92
D 169 137 169 85 154
2
All the twenty dairy cows were treated alike in all aspects expect the drugs administered to five dairy cows. Analyse the date at 1% level of significance. (6 marks)
d) Given v=6, b=4, msse= 15.31 and mssb=73.14. Estimate the relative efficiency of RBD and CRD e) Consider the following results of an experiment involving six treatment t1,t2......t6 in four randomized blocks B1, B2, B3 and B4.
Blocks Treatment and yield
B1 t1
24.7
t3
27.7
t2
20.6
t4
16.2
t5
16.2
t6
24.9
B2 t3
22.7
t2
28.8
t1
27.3
t4
15.0
t6
22.5
t5
17.0
B3 t6
26.3
t4
19.6
t1
38.5
t3
36.8
t2
39.5
t5
15.4
B4 t5
17.7
t2
31.0
t1
28.5
t4
14.1
t3
34.9
t6
22.6
At ? =0.05, test whether; (6 marks)
(i) Treatment differ significantly (ii) blocks differ significantly
QUESTION TWO (20 MARKS)
a) In the table given, are the yields of six varieties of wheat in a four replicate treatment for which one value is missing. Estimate the missing value and analyse the date. (12 marks)
3
Blocks Treatment
1 18.5 15.7 16.7 14.1 13.0 13.6
2 11.7 x 12.9 14.4 16.9 12.5
3 15.4 16.6 15.5 20.3 18.4 21.5
4 16.5 18.6 12.7 15.7 16.5 18.0
b) in the model = eij i ?? ??
where eij~N(o, ?
2 )
test DMRT is given by (8 marks)
t=
r msse yy j i 2 ?
QUESTION THREE (20 MARKS) a) From the statutual model ? ? ????? 2,0~, Neey ijkijkkjiijk ????? discuss the construction of ANOVA table of a latin square design (12 marks) b) Construct ANOVA table for the following latin square design (8 marks)
A1 A2 A3 A4
B1 t1=8 t2=15 t3=12 t4=6
B2 t4=10 t3=11 t2=10 t1=8
B3 t3=4 t4=5 t1=2 t2=1
B4 t2=3 t1=5 t4=2 t3=2
4
QUESTION FOUR
a) define the following (i) Contrast (2 marks) (ii) Orthogonal Latin Square design (4 marks) b) The plant manager has decided to run an experiment to determine whether the material received at different times has the same tensile strength 5 randomly chosen times
periods are to be considered and 5 randomly chosen men work on the material. The following are the results.
Men
1 2 3 4 5
Time period
1 7.5 11.8 17.6 8.8 17.9
2 21.4 12.9 12.4 15.0 20.6
3 16.0 9.7 7.4 18.4 16.6
4 16.0 18.3 23.6 27.4 25.2
5 23.3 30.5 25.8 24.5 26.6
(i) Test at 5% level of significant for homogeneity of the time periods and homogeneity of men (7 marks) (ii) Estimate the time period variability if it is significant (4 marks) (iii) What is the relative efficiency of this design compared to the CRD (3 marks)
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