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CHRIST (Deemed to be University),

Questions View-V Semester
Subject : STA541BN(DESIGN OF EXPERIMENTS)

U1--Analysis of variance

U1-T1-S1--Meaning and assumptions. Fixed, random and mixed effect models.

1 State the uses of two-way classified data with interaction effects along with example. 3.0 Medium Conceptual
(Applying/Analysing)
2 Write the structure of one-way ANOVA. 3.0 Complex(Evaluating/Creating) Analytical
3 What is fixed effect model? Give example. 3.0 Simple Conceptual
(Remembering/Understanding)
4 Write the structure of two-way ANOVA. 3.0 Medium Analytical
(Applying/Analysing)
5 Explain the test procedure of two-way ANOVA. 10.0 Medium Analytical
(Applying/Analysing)
6 Explain the test procedure of one-way ANOVA. 10.0 Simple Conceptual
(Remembering/Understanding)
7 Explain the test procedure of critical difference test. 10.0 Medium Analytical
(Applying/Analysing)
8 Explain the test procedure of two-way classified data with m-observation per cell. 10.0 Complex(Evaluating/Creating) Conceptual
9 What is the difference between ‘variability within classes’ and ‘variability between 6.0 Complex(Evaluating/Creating) Analytical
classes? Explain with a suitable example.
10 What is critical difference test? Write its uses. 6.0 Simple Analytical
(Remembering/Understanding)
11 Briefly explain the use of post-hoc analysis with example. 6.0 Medium Analytical
(Applying/Analysing)
12 How do you compare different treatment means using Tukey’s HSD test. 6.0 Medium Analytical
(Applying/Analysing)

U1-T2-S1--Analysis of variance of one-way and two-way classified data with and without interaction effects.

13What is mixed effect model? Give example. 3.0 Simple Conceptual

(Remembering/Understanding)
14Explain assignable and chance causes with example. 3.0 Complex(Evaluating/Creating) Conceptual
15State the assumptions of ANOVA. 3.0 Medium Analytical
(Applying/Analysing)
16What do you understand by ANOVA? 3.0 Medium Analytical
(Applying/Analysing)
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17A reputed marketing agency in India has three different training programs for its salesmen. The three 10.0 Simple Application
programs are method – A, B, C. To assess the success of the programs, 4 salesmen from each of the programs (Remembering/Understanding)
were sent to the field. Their performances in terms of sales are given in the following table.
Salesmen Methods

A B C

1 4 6 5

2 6 10 6

3 5 7 4

4 7 5 4

Test whether there is significant difference among methods and among salesmen. (Given: F(3, 6),0.05 =
4.7571, F(2, 6),0.05 = 5.1456).
18The illness caused by a virus in a city concerning some restaurant inspectors is not consistent with their 10.0 Medium Application
evaluations of cleanliness of restaurants. In order to investigate this possibility, the director has five restaurant (Applying/Analysing)
inspectors to grade the cleanliness of three restaurants. The results are shown below.
Inspector Restaurants

I II III

1 71 55 84

2 65 57 86

3 70 65 77

4 72 69 70

5 76 64 85

Carry out ANOVA at 5% level of significance. (Given: F(4, 8),0.05 = 3.838, F(2, 8),0.05 = 4.459).
19Following data show the birth-weights of babies born, classified according to the age of mother and order of 10.0 Complex(Evaluating/Creating) Application
gravida, there being three observations per cell:
Order of gravida Age-group of mother

15 − 20 20 − 25 25 − 30 30 − 35 35 and over

1 5.1, 5.0, 4.8 5.0, 5.1, 5.3 5.1, 5.1, 4.9 4.9, 4.9, 5.0 5.0, 5.0, 5.0

2 5.2, 5.2, 5.4 5.3, 5.3, 5.5 5.3, 5.2, 5.2 5.2, 5.0, 5.5 5.1, 5.3, 5.9

3 5.8, 5.7, 5.9 6.0, 5.9, 6.2 5.8, 5.9, 5.9 5.8, 5.5, 5.5 5.9, 5.4, 5.5

4 6.0, 6.0, 5.9 6.2, 6.5, 6.0 6.0, 6.1, 6.0 6.0, 5.8, 5.5 5.8, 5.6, 5.5

5 and over 6.0, 6.0, 6.0 6.0, 6.1, 6.3 5.9, 6.0, 5.8 5.9, 6.0, 5.5 5.5, 6.0, 6.2

Test whether the age of mother and order of gravida significantly affect the birth-weight. (Given: R.S.S. =
2351.19, F (4,50),0.05 = 2.57, F (16,50),0.05 = 2.13).
20A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the 10.0 Medium Analytical
production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the (Applying/Analysing)
results are shown in the following table:
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First Second
Machine
shift shift

M T W Th F M T W Th F

A 6 4 5 5 4 5 7 4 6 8

B 10 8 7 7 9 7 9 12 8 8

C 7 5 6 5 9 9 7 5 4 6

D 8 4 6 5 5 5 7 9 7 10

Perform an analysis of variance to determine at 5% level of significance, whether there is a difference (a)
between the machines and (b) between the shifts. (Given: F (1,32),0.05) = 4.15, F (3,32),0.05) = 2.90.
21Calculate critical difference for the following data 6.0 Simple Analytical
Mean
(Remembering/Understanding)
Source of Degree of Sum of
sum of F-cal F-tab t-tab
variation freedom square
square

Between
4 155.2 38.8 11.18 3.05 2.13
feeds

Within

feeds 15 52.0 3.47

(error)

Total 9 2.7.2

22Three different techniques namely medication, exercises and special diet are randomly assigned to 6.0 Medium Analytical
(individuals diagnosed with high blood pressure) lower the blood pressure. After four weeks the reduction in (Applying/Analysing)
each person’s blood pressure is recorded. Test at 5% level, whether there is significant difference in mean
reduction of blood pressure among the three techniques.
Medication 10 12 9 15 13

Exercise 6 8 3 0 2

Diet 5 9 12 8 4

(Given: F(2, 12),0.05 = 3.8853).

23In an experiment to determine the effect of nutrition on the attention spans of elementary school students, a 6.0 Medium Analytical
group of 15 students were randomly assigned to each of three meal plan: no breakfast, light breakfast and full (Applying/Analysing)
breakfast. Their attention spans (in min.) were recorded during a morning reading period and are shown as:
No breakfast 8 7 9 13 10

Light
14 16 12 17 11
breakfast

Full breakfast 10 12 16 15 12

Construct the analysis of variance table for this experiment. (Given: F(2,12),0.05=3.89)
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24Calculate least significant difference for the following data: 6.0 Complex(Evaluating/Creating) Analytical
Mean
Source of Degree of Sum of
sum of F-cal F-tab t-tab
variation freedom square
square

Treatment 2 250 125

Error 12 200 16.67 7.4985 3.89 2.18

Total 14 450

25 The varieties of coal were analysed by four chemist and the ash contents in the varieties was found as 10.0 Medium Application
varieties Chemists
(Applying/Analysing)
I II III IV

A 8 5 5 7

B 7 6 4 4

C 3 6 5 4

Analyse the data. (Given: F (2,6),0.05 = 5.14, F (3,6),0.05 = 4.76).

U1-T3-S1--Multiple comparison tests: Tukey's method, critical difference.

26 Write the total and error degree of freedom for two-way ANOVA. 3.0 Simple Application
(Remembering/Understanding)
27 What is random effect model? Give example. 3.0 Medium Analytical
(Applying/Analysing)
28 What are the various post-hoc tests ? 3.0 Medium Analytical
(Applying/Analysing)
29 Write the total, error and interaction degree of freedom for two-way ANOVA with m- 3.0 Complex(Evaluating/Creating) Application
observations per cell.

U2--Experimental designs

U2-T1-S1--Principles of design of experiments. Completely randomized, randomized block

30 What are the main uses of design of experiments ? 3.0 Complex(Evaluating/Creating) Analytical
31 State principles of design of experiments. 3.0 Medium Analytical
(Applying/Analysing)
32 What do you mean by experimental error? 3.0 Simple Analytical
(Remembering/Understanding)
33 State the limitations of completely randomized design. 3.0 Medium Analytical
(Applying/Analysing)
34 Explain blocks, yield and experimental unit in design of experiments. 6.0 Medium Analytical
(Applying/Analysing)
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35 How do you increase the efficiency of DOE? 6.0 Complex(Evaluating/Creating) Analytical

36 What do you mean by DOE? Write the important phases of every project. 6.0 Simple Analytical
(Remembering/Understanding)
37 Explain the importance of design of experiments in research. 6.0 Medium Analytical
(Applying/Analysing)
38 A manufacturing company has purchased three new machines of different makes and 10.0 Simple Application
wishes to determine whether one of them is faster than other in producing a certain (Remembering/Understanding)
output. Five hourly production figures are observed at random from each machine and
the results are given in the table below:
Sample
Machine
observations

A1 25 30 36 38 31

A2 31 39 38 42 35

A3 24 30 28 25 28

Analyse the data and check whether the machines are significantly different in their
mean speed. Use post hoc test if required. (Given: F (2,12),0.05 = 3.89, t (12),0.05 = 2.18)
39 A set of data involving four “tropical feed stuffs A, B, C, D” tried on 20 chicks is given 10.0 Medium Application
below. All the twenty chicks are treated a like in all respects except the feeding (Applying/Analysing)
treatments and each feeding treatment is given to 5 chicks
Gain in
Feed
weight

A 55 49 42 21 52

B 61 112 30 89 63

C 42 97 81 95 92

D 169 137 169 85 154

Analyse the data. (Given: F(3,16),0.05 = 3.06, t (16),0.05 = 2.12)

40 Consider the results given in the following table for an experiment involving six 10.0 Medium Application
treatments in four randomized blocks. The treatments are indicated by numbers within (Applying/Analysing)
parentheses
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1 (1) (3) (2) (4) (5) (6)

24.7 27.7 20.6 16.2 16.2 24.9

2 (3) (2) (1) (4) (6) (5)

22.7 28.8 27.3 15.0 22.5 17.0

3 (6) (4) (1) (3) (2) (5)

26.3 19.6 38.5 36.8 39.5 15.4

4 (5) (2) (1) (4) (3) (6)

17.7 31.0 28.5 14.1 34.9 22.6

Test whether the treatments differ significantly or not. (Given: F (3,15),0.05 = 5.42, F
(5,15),0.05 = 4.5).
41 The following data taken from a manurial experiment with sugarcane. The five 10.0 Complex(Evaluating/Creating) Application
treatments are as follows:
A: No manure
B: An inorganic manure
C, D and E: three levels of farm-yard manure.
Row Column

I II III IV V

I A E D C B

52.5 46.3 44.1 48.1 40.9

II D B A E C

44.2 42.9 51.3 49.3 32.6

III B A C D E

49.1 47.3 38.1 41.0 47.2

IV C D E B A

43.2 42.5 67.2 55.1 45.3

V E C B A D

47.0 43.2 46.7 46.0 43.2

Analyse the above data to find out if there are any difference in treatment effects.
(Given: F (4,2),0.05 = 5.41)
42 What is the historical perspective of design of experiments? 3.0 Simple Analytical
(Remembering/Understanding)

U2-T2-S1--Latin square designs (CRD, RBD, and LSD) -layout formation,

43 Justify need of randomization in design of experiment. 3.0 Complex(Evaluating/Creating) Analytical

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44 What are the requirements of good experimental design? 3.0 Simple Analytical
(Remembering/Understanding)
45 State the limitations of RBD. 3.0 Medium Analytical
(Applying/Analysing)
46 What is replication in design of experiment and state its role? 3.0 Medium Analytical
(Applying/Analysing)
47 Explain experiment and treatments in design of experiment. 6.0 Medium Analytical
(Applying/Analysing)
48 Explain the statistical analysis of RBD for one observation per experimental unit. 6.0 Complex(Evaluating/Creating) Analytical
49 Explain the statistical analysis of LSD. 6.0 Medium Analytical
(Applying/Analysing)
50 Explain the statistical analysis of CRD. 6.0 Simple Analytical
(Remembering/Understanding)

U2-T3-S1--analysis using fixed effect models.

51 Write the applications of CRD and RBD. 3.0 Medium Analytical

(Applying/Analysing)
52 Write the advantages of RBD. 3.0 Simple Analytical
(Remembering/Understanding)
53 Write the error and total degree of freedom in CRD, RBD and LSD. 3.0 Medium Analytical
(Applying/Analysing)
54 What do you understand by uniformity trials in design of experiments? 3.0 Complex(Evaluating/Creating) Analytical
55 Explain importance of local control in design of experiment. 3.0 Simple Analytical
(Remembering/Understanding)
56 What are disadvantages of Latin square design? 3.0 Medium Analytical
(Applying/Analysing)

U3--Efficiency of a design and missing plot technique

U3-T1-S1--Comparison of efficiencies of CRD, RBD,

57 Give the expression for the relative efficiency of Latin square design of order K over 3.0 Medium Analytical
RCBD. (Applying/Analysing)
58 Write the error degree of freedom and total degree of freedom when one observation is 3.0 Medium Analytical
missing in RBD. (Applying/Analysing)
59 State the properties of Latin square design. 3.0 Complex(Evaluating/Creating) Analytical
60 Write formulae used to calculate efficiency RCBD over a CRD and explain the terms. 3.0 Simple Analytical
(Remembering/Understanding)
61 Following is the yield of 6 variates in a 4-replicate experiment for which one value is 6.0 Complex(Evaluating/Creating) Analytical
missing. Estimate the missing value
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Blocks Treatments

1 2 3 4 5 6

1 18.5 15.7 16.2 14.1 13.0 13.6

2 11.7 ⋯ 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

62 Explain the estimation of missing value in RBD. 6.0 Medium Analytical

(Applying/Analysing)
63 Derive the efficiency of RBD relative to CRD. 6.0 Simple Analytical
(Remembering/Understanding)
64 How we will estimate two missing observations in RBD? 6.0 Medium Analytical
(Applying/Analysing)
65 Determine the missing value 6.0 Complex(Evaluating/Creating) Application
D B C A

20.1 19.4 30.6 7.9

C A D B

17.5 10.4 21.2 19.1

A D B C

? 18.1 24.6 25.2

B C A D

25.1 30.4 10.2 28.0

66 Derive the efficiency of LSD relative to RBD. (Columns of LSD as blocks). 6.0 Medium Analytical
(Applying/Analysing)
67 Derive the efficiency of LSD relative to RBD. (Row of LSD as blocks). 6.0 Medium Analytical
(Applying/Analysing)
68 Explain the estimation of missing values in Latin square design. 6.0 Simple Analytical
(Remembering/Understanding)

U3-T2-S1--Estimation of single missing observation in RBD and LSD and analysis.

69 State the importance of missing plot technique in design of experiment. 3.0 Medium Analytical
(Applying/Analysing)
70 Explain the importance of estimation of missing value in design of experiment. 3.0 Complex(Evaluating/Creating) Analytical
71 What are the demerits of Latin square design? 3.0 Simple Analytical
(Remembering/Understanding)
72 How do you calculate upward bias in estimating missing value of Latin square design 3.0 Medium Analytical
of order k? (Applying/Analysing)
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U3-T3-S1--Comparison of efficiencies of LSD.

73 Write the formula used in comparison of efficiency of LSD over RBD. 3.0 Medium Analytical
(Applying/Analysing)
74 Make the ANOVA table for CRD (Random effect model) that we use in efficiency 3.0 Simple Analytical
comparison of RBD over CRD. (Remembering/Understanding)
75 List the importance of data transformation in design of experiment. 3.0 Complex(Evaluating/Creating) Analytical
76 List the changes need to be made in analysis of design of experiment after estimating 3.0 Medium Analytical
missing value. (Applying/Analysing)

U4--Factorial experiment

U4-T1-S1--Factorial experiment: Basic concepts, main effects, interactions, and orthogonal contrasts in 22 and 23 factorial experiments. Yates' method of computing
factorial effects total.

77 Explain how factorial experiment is different from Latin square design with respect to 3.0 Complex(Evaluating/Creating) Analytical
general model.
78 State importance of factorial experiment in research. 3.0 Medium Analytical
(Applying/Analysing)
79 List the applications of factorial experiment. 3.0 Medium Analytical
(Applying/Analysing)
80 Explain factorial experiment with example. 3.0 Simple Analytical
(Remembering/Understanding)
81 Explain simple effect of 2n factorial experiment. 10.0 Medium Conceptual
(Applying/Analysing)
82 Explain the importance of factorial experiment with confounding in field of research 10.0 Simple Conceptual
with suitable examples. (Remembering/Understanding)
83 Explain interaction effect of 2n factorial experiment. 10.0 Medium Conceptual
(Applying/Analysing)
84 Give the method of calculating sum of squares for factorial effects in general with 10.0 Complex(Evaluating/Creating) Conceptual
suitable example.

U4-T2-S1--Analysis and testing the significance of effects in 22 and 23 factorial experiments in RBD. Need for confounding.

85 What are symmetrical and asymmetrical factorials? 3.0 Medium Analytical

(Applying/Analysing)
86 Write formula for calculation of main effect and interaction effect in 23 factorial 3.0 Complex(Evaluating/Creating) Conceptual
experiment.
87 State the limitations of factorial experiments. 3.0 Simple Analytical
(Remembering/Understanding)
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88 Write two suitable real-life examples for 23 factorial experiment. 3.0 Medium Conceptual
(Applying/Analysing)
89 State of hypothesis of 23 factorial experiment. 6.0 Simple Analytical
(Remembering/Understanding)
90 Explain how factorial different is different from Latin Square Design. 6.0 Complex(Evaluating/Creating) Critical
91 Write the general model and state of hypothesis of 22 factorial experiment. 6.0 Medium Analytical
(Applying/Analysing)
92 Write the general model and ANOVA structure of 23 factorial experiment. 6.0 Medium Conceptual
(Applying/Analysing)
93 Explain steps involved in analysis of 23 factorial experiment in RCBD with r 10.0 Medium Conceptual
replications. (Applying/Analysing)
94 Explain the steps involved in analysis of 22 factorial experiment in CRD. 10.0 Medium Conceptual
(Applying/Analysing)
95 Fill the ANOVA table and give your conclusions 10.0 Complex(Evaluating/Creating) Conceptual
Source of
df SS MS F0
variation

Blocks 7 678.4667

N 1 124.0312

P 1 30.0312

K 1 30.0312

NP 1 34.0312

NK 1 0.0312

PK 1 26.2812

Error 18 411.8125

Total 31 1334.7167

96 Explain steps involved in analysis of 23 factorial experiment in RCBD. 10.0 Simple Conceptual
(Remembering/Understanding)
97 Using Yates’ algorithm for 22 experiments, compete the following table: 10.0 Medium Application
(Applying/Analysing)
Treatment
Total
combination (3) (4)
(2)
(1)

(1) [1]

a [a]

b [b]

ab [ab]

U4-T3-S1--Complete and partial confounding in a 23 factorial experiment in RBD - layout and its analysis.
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98 When do you call partial confounding as balance and unbalanced confounding? 3.0 Medium Analytical
(Applying/Analysing)
99 Differentiate between complete and partial confounding with example. 3.0 Medium Conceptual
(Applying/Analysing)
100 List the differences between balanced and unbalanced confounding with example. 3.0 Simple Conceptual
(Remembering/Understanding)
101 List the importance of confounding in analysis of factorial experiment. 3.0 Complex(Evaluating/Creating) Analytical