**[OBJECTIVE]**

**Subject:** Design and Analysis of Experiments in Research

**Time Allowed:** 15 Minutes

**Maximum Marks:** 10

**NOTE:** *Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.*

__Part-I Encircle the right answer, cutting and overwriting are not allowed. (10)__

1. The basic principles of experimental designs consist of:

a) Randomization

b) Replication

c) Local Control

d) All of these

2. The smallest subdivision of the experimental material is called:

a) Treatments

b) Experimenta! Unit

c) Expesimenta! Error

d) None of these

3. In a completely randomized design, treatments are assigned to experimental units ________ at random.

a) Completely

b) Partially

c) Systematically

4. The assumptions under unalysis of variance consist of:

a) Normality and Independence

b) Both (a) and (b)

c) Linearity and Additivity

d) None of these

5. The following design provides the maximum number of degrees of freedom for error sum of squares:

a) Completely Randomized Design

b) Latin Square Design

c) Completely Randomized Block Design

d) None of these

6. Multiple comparisons tests are applicable when:

a) Null Hypothesis about equality of means is rejected

b) Nul. Hypotnesis about equality of means is accepted

c) Does not depend upon the rejection or acceptance of Nul! Hypothesis

d) None ofthese

7. One can estimate the missing observation through covariance technique by simply changing the sign of….

a) b

b) r

c) Correction Factor

d) None of these

8. The efficiency of two experimental designs can simply be measurcd through _______ of error variances.

a) Addition

b) Subtraction

c) Multiplication

d) Ratio

9. Two Latin squares are _________ if each letter of one square design occurs exactly once with every letter of the other square when they are superimposed.

a) Orthogonal

b) Factorial Designs

c) Efficient

d) None of these

10. A contrast is _______ combination of treatments.

a) Linear

b) Exponential

c) Quadratic

d) None of these

**[SUBJECTIVE]**

**Subject:** Design and Analysis of Experiments (Theory)

**Time Allowed:** 2 Hours 45 Minutes

**Maximum Marks:** 50

**NOTE:** *ATTEMPT THIS (SUBJECTIVE) ON THE SEPARATE ANSWER SHEET PROVIDED.*

__Part-II Give short notes on following, each question carries equal marks. (20)__

**Q#1:** Fixed Effects and Random Effects.

**Q#2:** Analysis of Variance and Covariance.

**Q#3:** Completely Randomized and Completely Randomized Block Designs

**Q#4:** Replication and Randomization.

**Q#5:** Latin Square and Graeco Latin Square Designs.

__ __

__Part-III Give detailed answers, each question carries equal marks. (30)__

**Q#1:** a) In an experimen ‘k’ treatments and ‘r’ blocks are selected at random from a large number of treatments and dlocks. Develop expected mean Squares by clearly indicating the assumptions used.

- b) Given the following ANOVA for a CR cesign for four treatments:

**S.O.V** d.f SS

**Treatments** 3 1.1986

**Error** 36 1.0323

Test the significance of difference between treatment means by using Duncan’s Multiple Range

Test when treatment means for four treatinents were 1.464, 1.195, 1.325, and 1.66.

**Q#2:** Seven treatments arranged in six randomized complete blocks gave the following sum of squares and products:

**S.O.V** X.Y Y.Y X.X

Blocks -111.65 6.31 7472.6

**Treatments** 3598.05 112.86 116020.3

**Error** 36 1.0323 28665.1

- i) Is the regression of Y on X Significant at 0.05 level of significance.
- ii) Construct ANOVA and write the inference.

**Q#3:** a) Derive formula for estimating N missing observations in a Latin Square Design when values are missing in different columns. different tows and different treatments.

- b) In an experiment to examine the effects of row spacing on the yield of wheat, 8 row spacing were used and 6 blocks of an experiment were used. The sum of squares for Total, Blocks and Treatments were 2195.48, 6:7.86 and 1283.65 respectively. Find the relative efficiency of this design with the design in which blocks are ignored.