Below is given the plan and yields of 22 -Factorial Experiment involving 2 factors A and B each at two levels 0 and 1. Analyse the design
| Block I | |||
| 117 (1) | 106 b | 129 ab | 124 a |
| Block II | |||
| 124 ab | 120 (1) | 117 b | 124 a |
| Block III | |||
| 111 (1) | 127 a | 114 b | 126 ab |
| Block IV | |||
| 125 ab | 131 a | 112 b | 108 (1) |
| Block V | |||
| 95 ab | 97 b | 73 (1) | 128 a |
| Block VI | |||
| 158 a | 81 (1) | 125 ab | 117 b |
Does treatment effect A differs from treatment effect B?
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Define the difference estimator for the population mean. Show that it is an unbiased estimator and its variance is given by where symbols have their usual meanings.
Suppose we wish to estimate the total number of Cows in 2026 in certain state. The total number of cows for 2024 was X = 5000. The Sampling unit was the farm, and it is assumed that there has been no change in the number of farms which we shall assume to be N=500. A sample of n=20 farms is selected, and the data is as follows:
| Farm | 2024 | 2026 | Farm | 2024 | 2026 |
| 1 | 12 | 14 | 11 | 11 | 14 |
| 2 | 22 | 25 | 12 | 17 | 19 |
| 3 | 38 | 37 | 13 | 12 | 12 |
| 4 | 15 | 18 | 14 | 22 | 23 |
| 5 | 18 | 20 | 15 | 14 | 16 |
| 6 | 31 | 30 | 16 | 26 | 28 |
| 7 | 15 | 15 | 17 | 08 | 09 |
| 8 | 20 | 21 | 18 | 16 | 15 |
| 9 | 10 | 12 | 19 | 13 | 15 |
| 10 | 25 | 12 | 20 | 19 | 20 |
Let us consider the following Balanced Incomplete Block Design (B.I.B.D.) with parameters
| Block Label | Design |
| I | 1 3 4 5 |
| II | 1 4 6 7 |
| III | 1 2 5 7 |
| IV | 3 5 6 7 |
| V | 2 3 4 7 |
| VI | 1 2 3 6 |
| VII | 2 4 5 6 |
A population consisting of 6 clusters, each of size 6 is given below. The values of the study variable Y, noted on each of the units within each cluster are also provided. A random sample of size 3 clusters was selected from the population and 3 elementary units from the selected clusters were randomly chosen
| Cluster | Y - values | Cluster | Y - values |
| 1 | 2, 4, 6, 1, 3, 5 | 4 | 3, 2, 5, 1, 6, 4 |
| 2 | 2, 5, 3, 4, 7, 4 | 5 | 2, 4, 6, 8, 3, 5 |
| 3 | 4, 3, 6, 2, 1, 5 | 6 | 4, 1, 2, 7, 5, 3 |
Define the Residual B.I.B.D. and Derived B.I.B.D. of a given symmetric B.I.B.D. Mention the rule of constructing a residual B.I.B.D. corresponding to a specific B.I.B.D.
then (X, ) is a (5, 3, 3)- B.I.B.D. Find the incidence matrix of this B.I.B.D.
Below is given the plan and yields of 22 -Factorial Experiment involving 2 factors A and B each at two levels 0 and 1. Analyse the design
| Block I | |||
| 117 (1) | 106 b | 129 ab | 124 a |
| Block II | |||
| 124 ab | 120 (1) | 117 b | 124 a |
| Block III | |||
| 111 (1) | 127 a | 114 b | 126 ab |
| Block IV | |||
| 125 ab | 131 a | 112 b | 108 (1) |
| Block V | |||
| 95 ab | 97 b | 73 (1) | 128 a |
| Block VI | |||
| 158 a | 81 (1) | 125 ab | 117 b |
Explain what is meant by a one-quarter fractional factorial experiment of a 2 2 factorial experiment. Give a notation which denotes the one-quarter fractional factorial design.