Generate a complete cycle for the LCG given xi = (12 xi-1 + 6) Mod 11 with x0 = 06 . A man tosses an unbiased coin 10 times. Using the first 10 random numbers generated above, obtain a sequence of heads and tails.
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Suppose from a total of 20 bearing trees of Guava in a village, 5 clusters of size 4 trees each were selected and Yield (in Kgs) is a given in the following table:
| Cluster | 1st Tree | 2nd Tree | 3rd Tree | 4th Tree |
| 1 2 3 4 5 | 5 11 36 7 2 | 4 1 10 15 22 | 1 4 19 12 8 | 15 7 11 10 6 |
i) ) cluster totals
ii) ) cluster Means
iii) Population Mean per Cluster and
iv) , i.e., Population Mean Per Unit
Below are given the weights of 5 students:
| S. No | 1 2 3 4 5 |
| Weights (Kg) | 56 49 66 64 55 |
i) Sample mean ()is unbiased for Population mean
iii)
Following U(0,1) were generated by a random number generation method:
| 251
597
449
464 | 769
729
998
447 | 153
012
919
279 | 575
922
470
413 | 390
691
372
494 | 335
817
851
972 | 066
064
643
983 | 104
539
509
432 | 200
419
913
368 | 019
305
445
574 |
The height of the plants are given in the table given below for an experiment involving six treatments in four randomised blocks. The treatments are indicated by numbers with brackets:
| Blocks | Heights of Plants (cms) | |||||
| I | (1) 24.7 | (3) 27.7 | (2) 20.6 | (4) 16.2 | (5) 16.2 | (6) 24.9 |
| II | (3) 22.7 | (2) 28.8 | (1) 27.3 | (4) 15 | (6) 22.5 | (5) 17 |
| III | (6) 26.3 | (4) 19.6 | (1) 38.5 | (3) 36.8 | (2) 39.5 | (5) 15.4 |
| IV | (5) 17.7 | (2) 31 | (1) 28.5 | (4) 14.1 | (3) 34.9 | (6) 22.6 |
Select a sample of 3 cluster and calculate the sample cluster mean c
State whether the following statements are true or false and also give the reason in support of your answer:
a) If the SSE in a two way ANOVA having 4 rows and 5 columns is given as 48, then the MSSE will be 4.
b) If there is one missing value in RBD with 3 blocks and 4 treatments, then the total of degrees of freedom will be 10.
c) In a sequence of random numbers, generated through LCG”
x i = (5 x (i-1) + 3) Mod(16), with
x 0 = 5" the x1 , x2 and x3 will be 11, 14, 13.
d) The probability of selection of a sample of n from the population by SRSWOR is 1/ Nn .
e) In 23 factorial design, there 2 factors each at 3 levels.
An Investigator is interested in finding the level of knowledge about the history of India of 4 different schools in a city. A test is given to the 5, 6, 7, 6 students of 8th class of 4 schools, respectively. Their scores out of 10 are given as below:
|
School I: School II: School III: School IV: |
8
6
6
5 |
6
4
5
6 |
7
6
5
6 |
5
5
6
7 |
9
6
7
6 |
7
8
7 |
5
|