LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2006

                                       ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

(Also equivalent to STA 600)

 

 

Date & Time : 19-04-2006/FORENOON     Dept. No.                                                       Max. : 100 Marks

 

 

Part – A

Answer all the questions.                                                                      10 ´ 2 = 20

 

1. Define mixed effect model.
2. Define orthogonal contrast.
3. What is an experimental unit?
4. Define uniformity trial.
5. What do you mean by randomized block design?
6. Write any two advantages of completely randomized design.
7. Under what conditions can LSD be used?
8. When a BIBD is called symmetric?
9. Define resolvable design.
10. What is the need for factorial experiments?

Part – B

 

Answer any five questions.                                                                     5 ´ 8 = 40

 

11. Explain the basic principles in the design of experiments.
12. Compute the least square estimates of randomized block design
13. A randomized block experiment has been carried out in 4 blocks with 5 treatments A, B, C, D and E. The reading for treatment B in block 2 is missing. Explain the procedure of obtaing the estimate of one missing observation in the above design.
14. Complete the following table for the analysis of variance and give your conclusion.

Source of variance	Sum of square	D. F	M.S.S	Variance Ratio
R C T Error	46.67 —– —– —–	4 —– —– —–	—– —– 49.152 2.336	—– 1.500 —–
Total	—–	—–

 

15. How do you compute effects of totals using Yate’s method for 3²?
16. Derive main effects and interaction effects for 2² factorial experiments.
17. From the following table, find out the confounded treatment combinations

Block	Replication I		Replication II		Replication III		Replication IV
	1	2	3	4	5	6	7	8
	abc a b c	ab ac bc (1)	abc ab c (1)	ac bc a b	abc bc a (1)	ab ac b c	Abc Ac B (1)	ab bc a c

 

18. Prove that l (v – 1) = r (k-1) for a BIBD.

 

Part – C

 

Answer any two questions.                                                                   2 ´ 20 = 40

 

19. Explain the analysis of variance table for a one-way layout dealing with homogeneity of data relative to k groups in detail.
20. Give the complete statistical analysis of Latin square design
21. Analyze the following 2³ completely confounded factorial design.

	Block 1				Block 2
Replicate 1	‘1’ 101	(nk)291	(np)373	(kp)391	(nkp)450	(n)106	(k)265	(p)312
	Block 3				Block 4
Replicate 2	‘1’ 106	(nk)306	(np)338	(kp)407	(nkp)449	(n)189	(k)272	(p)324
	Block 5				Block 6
Replicate 3	‘1’ 187	(nk)334	(np)324	(kp)423	(nkp)417	(n)128	(k)279	(p)323
	Block 7				Block 8
Replicate 4	‘1’ 131	(nk)272	(np)361	(kp)245	(nkp)437	(n)103	(k)302	(p)324

 

22. a). State and prove Fisher’s inequality in BIBD.

b). Obtain the analysis of a BIBD using intra block information.            (10 +10)

 

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