A researcher wants to test four diets A, B, C, D on growth rate in mice. These animals are divided into 3 groups according to their weights. Heaviest 4, next 4 and lightest 4 are put in Block I, Block II, and Block III, respectively. Within each block, one of the diets is given at random to the animals. After 15 days, increase in weight is noted, which is given in the following table:

Identify the design given in the following table and then carry out the analysis:

Draw all possible samples of size 2 from the population [2, 3, 4] and verify that E ( x̄ ) = x̄  . find variance of x̄

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:

The distribution function of Pareto distribution is given by f(x) = 1 - (k/x)^a   , a >0 , 0 < k ≤ x.
Given a U~ U(0, 1), generate a random number from the above distribution, when a = 2 and k = 1. Suppose U = 0.5, then find x

Times between successive crashes of a computer system were generated for a 6-month period and are given in increasing order as follows (time in hours):

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