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To analyze the data from the manurial trial and draw conclusions, we will perform an Analysis of Variance (ANOVA) test. This test will help us determine whether there are significant differences among the six levels of Farmyard Manure (FYM) and whether the variations in cotton yield per plot can be attributed to these different levels.

First, let's organize the data in a table:

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Levels of FYM	Replications	Cotton Yield (Kg)
1	I	6.90
1	II	6.48
1	III	6.52
1	IV	6.90
2	I	4.60
2	II	5.57
2	III	7.60
2	IV	6.65
3	I	4.40
3	II	4.28
3	III	5.30

Levels of FYM	Replications
	I             II         III          IV
1 2 3 4 5 6	6.90      4.60    4.40     4.81 6.48      5.57    4.28     4.45 6.52      7.60    5.30     5.30 6.90      6.65    6.75     7.75 6.00      6.18    6.50     5.50 7.90      7.57    6.80     6.62

Carry out the Analysis of Variance test and draw the conclusions.

In order to compare the mileage yields of 3 kinds of Gasoline, several tests were run, and the following results were obtained:

Gasoline A:	19	21	20	18	21	21
Gasoline B:	23	20	22	20	24	23
Gasoline C:	20	17	21	19	20	17

Carry out the Analysis of Variance test and test whether there is significant differences between the average mileage of 3 kinds of gasoline at 5% level of significance.

For the given data the yield of the treatment 2 in 3rd block is missing. Estimate the missing value and analyse the data.

Treatments	Blocks
1 2 3	I               II           III            IV
	105          114        108         109 112          113         Y           112 106          114        105         109

 

A sample of 100 employees is to be drawn from a population of collages A and B. The population means and population mean squares of their monthly wages are given below:

Village	Ni	Xi	Si2
Collage A	400	60	20
Collage B	200	120	80

Draw the samples using Proportional and Neyman allocation techniques and compare. Obtain the sample mean and variances for the Proportional Allocation and SRSWOR for the given information. Then Find the percentage gain in precision of variances of sample mean under the Proportional Allocation over the that of SRSWOR.

In a class of Statistics, total number of students is 30. Select the linear and circular
systematic random samples of 12 students. The age of 30 students is given below:
Age: 22 25 22 21 22 25 24 23 22 21 20
21 22 23 25 23 24 22 24 24 21 20
23 21 22 20 20 21 22 25

In a population of size N = 5, the values of the population characteristics are 1, 3, 5, 7, 9, a sample of size 2 is drawn. Verify that y is an unbiased estimate of YandV(y) is equal to

V(y)=

State whether the following statements are true or false and also give the reason in
support of your answer: (5×2=10)
(a)Vopt( _st )lies betweenV_prop andV (X_st ).and V_{Random (}X_st).
(b) The total number of all possible samples of size 3 without replacement from a population of size 7 is 21.
(c) While analysing the data of a 5 × 5 Latin Square design the d.f. for ESS is equal
to 16.
(d) In a Two-way Analysis of Variance test with 5 observations per cell having 4
blocks and 4 treatments the degree of freedom for the total variation is 64.
(e) The probability of selection of a sample of n from the population by SRSWOR is
1/ N.