Identify the design given in the following table and then carry out the analysis:
| Column | Row | |||
|---|---|---|---|---|
| I | II | III | IV | |
| I | A 8 | C 18 | B 11 | D 8 |
| II | C 16 | B 10 | D 7 | A 4 |
| III | B 12 | D 10 | A 6 | C 20 |
| IV | D 10 | A 9 | C 28 | B 16 |
The given table represents a two-factor factorial design with four levels for each factor. Factor A has levels I, II, III, IV for rows, and Factor B has levels I, II, III, IV for columns. The numbers in each cell represent the observed response, while the letters indicate a treatment combination label. First, we extract the observed values in a clear matrix format: | | I | II | III | IV | | --- | -- | -- | --- | -- | | I | 8 | 18 | 11 | 8 | | II | 16 | 10 | 7 | 4 | | III | 12 | 10 | 6 | 20 | | IV | 10 | 9 | 28 | 16 | Step 1: Compute the row totals and column totals * Row totals: * I: 8 __________ _________ _______ _________ _________.
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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 |
The distribution function of Pareto distribution is given by ,
.
Given a , generate a random number from the above distribution, when
and
.
Suppose , 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):
1 10 20 30 40 52 63 70 80 90 100 102
130 140 190 210 266 310 530 590 640 1340
The parameter , mean
.
Use the Kolmogorov-Smirnov test to examine the goodness of fit of exponential distribution.
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 |
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:
| Blocks | Treatments/Diets | |||
|---|---|---|---|---|
| A | B | C | D | |
| I | 12 | 8 | 6 | 5 |
| II | 15 | 12 | 9 | 6 |
| III | 14 | 10 | 8 | 5 |
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.