The following data is the data pertaining to a feeding trial on sheep.

Question

The following data is the data pertaining to a feeding trial on sheep. Treatments

A: Grazing only
B: Grazing + Maize Supplements
C: Grazing + Maize + Protein Supplement P₁
D: Grazing + Maize + Protein Supplement P₂
E: Grazing + Maize + Protein Supplement P₃

Layout and Wool Yield (100 gm) is given as:

24 Apr 2024

Answer :

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State whether the following statements are true or false and also give the reason in support of your answer:

(a) $V_{opt}\left ( \bar{X_s_t} \right )$ lies between $V_{prop}\left ( \bar{X}_{st} \right )$ and. $V_{Random}\left ( \bar{X}_{st} \right ).$ prop st Random st

(b) The total number of all possible samples of size 3 without replacement from a population of size 7 is 21.

(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.

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

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 $\bar{y}$ is an unbiased estimate of $\bar{Y}$ andV( $\bar{y}$ ) is equal to

$\bg_white V(\bar{y})=\frac{N-n}{Nn}S^2.$

A manurial trial with six levels of Farmyard Manure (FYM) was carried out in a randomised block design with 4 replications at the experimental station Junagarh with a new study the rate of decomposition of organic matters in soil and its synthetic capacity in soil on cotton crop. The yield per plot in kg for different levels of FYM and replications is given below:

Cotton Yield Per Plot (in Kg)

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

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

The following data is the data pertaining to a feeding trial on sheep. Treatments

A: Grazing only
B: Grazing + Maize Supplements
C: Grazing + Maize + Protein Supplement P₁
D: Grazing + Maize + Protein Supplement P₂
E: Grazing + Maize + Protein Supplement P₃

Layout and Wool Yield (100 gm) is given as:

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.

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	$\bar{X_i}$	$S_{i}^{2}$
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.

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