In the following data, two values are missing. Estimate these values by Yates method and analyse the data by suitable technique.
| Treatments | Blocks | ||
|---|---|---|---|
| I | II | III | |
| A | 12 | 14 | 12 |
| B | 10 | y | 8 |
| C | x | 15 | 10 |
The data form a randomized block design with three treatments and three blocks, with two missing observations: one for treatment B in block II (y) and one for treatment C in block I (x). By Yates’ method, each missing value is estimated by equating it to the value that would make the treatment and block totals consistent with the additive model. Let the missing values be x (C, I) and y (B, II). First write the treatment totals and block totals in terms of x and y. Treatment totals: A = 12 + 14 + 12 = 38 B _______ ________ ______ _____ ________ _________.
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To determine the yield rate of wheat in a district of Punjab, 6 groups of 6 plots each were constructed. The data are given in the following table:
| Plot No. | Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | Group 6 |
|---|---|---|---|---|---|---|
| 1 | 8 | 6 | 18 | 13 | 17 | 12 |
| 2 | 13 | 5 | 8 | 7 | 15 | 15 |
| 3 | 11 | 16 | 6 | 13 | 10 | 11 |
| 4 | 26 | 5 | 10 | 6 | 21 | 17 |
| 5 | 13 | 16 | 16 | 7 | 20 | 8 |
| 6 | 31 | 5 | 20 | 2 | 25 | 10 |
Generate a complete cycle for the LCG given below: , with
. A man tosses an unbiased coin ten times. Using the first ten random numbers generated above, obtain a sequence of heads and tails by taking Head (H) as
.
The following data relate to production in kg of three varieties P, Q, R of wheat:
| P : | 14 | 16 | 18 | ||
| Q: | 14 | 13 | 15 | 22 | |
| R : | 18 | 16 | 19 | 15 | 20 |
A sample of 60 students is to be drawn from a population consisting of 600 students belonging to two villages, A and B. The means and standard deviations of their marks are give below:
| Villages | Stratum sizes ($N_i$) | Means ($x_i$) | Standard deviations |
|---|---|---|---|
| Village A | 400 | 60 | 20 |
| Village B | 200 | 120 | 80 |
In the following data, two values are missing. Estimate these values by Yates method and analyse the data by suitable technique.
| Treatments | Blocks | ||
|---|---|---|---|
| I | II | III | |
| A | 12 | 14 | 12 |
| B | 10 | y | 8 |
| C | x | 15 | 10 |
State whether the following statements are true or false and also give the reason in support of your answer:
(a) The total number of all possible samples of size 2 without replacement from a population of size 7 is 21.
(b) Consecutive 3 random numbers starting from 8937 by 'middle square method' are 8937, 8699, 6726.
(c) RBD is suitable in situations where it is not possible to divide the experimental material into a number of homogeneous blocks.
(d) As we increase the sample size, representativeness of the population by the sample decreases.
(e) In a big hall, there are 50 rows and each row has 60 students. A research scholar selects 10 rows randomly and then randomly selects 15 students from each selected row. It is an example of cluster sampling procedure.
Draw all possible samples of size 2 from the population [2, 3, 4] and verify that . Also find variance of
.