Below are given the weights of 5 students:
| S. No | 1 2 3 4 5 |
| Weights (Kg) | 56 49 66 64 55 |
a) Calculate Population Mean, Population mean square and Population Variance.
b) Enumerate all possible samples of size 2 without replacement and show that
i) Sample mean ()is unbiased for Population mean
ii) Sample mean square (s2) is unbiased for the Population Mean Square (S2)
iii)
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Below is given the plan and yields of 22 factorial experiment involving 2 factors A and B each at two levels 0 and 1:
| Block I | (1) 117 | b 106 | ab 129 | a 124 |
| Block II | ab 124 | (1) 120 | b 117 | a 124 |
| Block III | (1) 111 | a 127 | b 114 | ab 126 |
| Block IV | ab 125 | a 131 | b 112 | (1) 108 |
| Block V | ab 95 | b 97 | (1) 73 | a 128 |
| Block VI | a 158 | (1) 81 | ab 125 | b 117 |
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
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.
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)
The following data represent the number of units of production per day turned out by 5 different workers using four different types of machines:
| Workers | Machine Type | |||
| A | B | C | D | |
| 1 2 3 4 5 | 54 56 44 53 48 | 48 50 46 48 52 | 57 62 54 56 59 | 46 53 42 43 49 |
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 |
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.