IGNOU MST 13 SOLVED ASSIGNMENT

Included:

MST 013 (January 2025 - July 2025) - ENGLISH

TUTOR MARKED ASSIGNMENT

MST-013: Survey Sampling and Design of Experiments-l

Course Code: MST-013

Assignment Code: MST-013/TMA/2025

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

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

(a) 

(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

2(a) 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		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.

(b) A population consists of 10 villages with a total of 212 households. The second column of the accompanying table shows the number of households corresponding to each village. Select a PPS with replacement sample of 6 villages by using the Cumulative Total method:

Village	1	2	3	4	5	6	7	8	9	10
No. of Households	35	28	20	25	30	19	10	12	18	15

3(a) 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  is an unbiased estimate of and  is equal to

(b) 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

4(a) 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
	I	II	III	IV
1	6.90	4.60	4.40	4.81
2	6.48	5.57	4.28	4.45
3	6.52	7.60	5.30	4.45
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. 

(b) 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
	I	II	III	IV
1	105	114	108	109
2	112	113	Y	112
3	106	114	105	109

 

5(a) 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:

32(D)	33(E)	30(C)	28(B)	24(A)
51(C)	45(D)	41(A)	45(E)	29(B)
41 (E)	29 (A)	24 (B)	36 (D)	35 (C
38 (B	39(C)	42(E	23(A)	37(D)
38(A	24(B)	21(D)	29(C)	26(E)

Analyse the design with appropriate method and calculate the Critical Difference for the treatment mean yield

(b) 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

 

MST 013 (January 2026 - July 2026) - ENGLISH

Course Code: MST-013

Assignment Code: MST-013/TMA/2026

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

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

(2×5=10)

a) The total number of all possible samples of size 2 without replacement from a population of size 7 is 49.

b) RBD is suitable in situations where it is not possible to divide the experimental material into a number of homogeneous blocks.

c) If experimental error is reduced considerably and the efficiency of the design is decreased.

d) If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.

e) As we increase the sample size, representativeness of the population by the sample decreases.

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

(b) 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: 

Based on the image provided, here is the data organized into a clear table:

Villages	Stratum sizes ($N_i$)	Means ($x_i$)	Standard deviations
Village A	400	60	20
Village B	200	120	80

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What are the sample sizes for the two villages using proportional allocation technique?

3.(a) A population consists of 10 villages with a total of 212 households. The second column of the accompanying table shows the number of households corresponding to each village. Select a PPS with replacement sample of 6 villages by using the Cumulative Total method:

I've transcribed the data from the image into a clean Markdown table for you.

Household Distribution by Village

Village	1	2	3	4	5	6	7	8	9	10
No. of Households	35	28	20	25	30	19	10	12	18	15

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(b) 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.                  

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4.    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

Is there any significant difference among the three varieties at 5% level of significance? (10)

5. 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

Perform a two-way ANOVA to test whether the data indicates any significant difference between the four diets due to different blocks. (10)

6. In the following data, two values are missing. Estimate these values by Yates method and analyse the data by suitable technique.

---

the data by suitable technique.

Treatments	Blocks
	I	II	III
A	12	14	12
B	10	y	8
C	x	15	10

7.(a) 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

<p align="right">(14)</p>

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(b) 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

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MST 013 (January 2025 - July 2025) - ENGLISH

TUTOR MARKED ASSIGNMENT

MST-013: Survey Sampling and Design of Experiments-l

Course Code: MST-013

Assignment Code: MST-013/TMA/2025

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

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

(a) 

(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

2(a) 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		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.

(b) A population consists of 10 villages with a total of 212 households. The second column of the accompanying table shows the number of households corresponding to each village. Select a PPS with replacement sample of 6 villages by using the Cumulative Total method:

Village	1	2	3	4	5	6	7	8	9	10
No. of Households	35	28	20	25	30	19	10	12	18	15

3(a) 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  is an unbiased estimate of and  is equal to

(b) 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

4(a) 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
	I	II	III	IV
1	6.90	4.60	4.40	4.81
2	6.48	5.57	4.28	4.45
3	6.52	7.60	5.30	4.45
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. 

(b) 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
	I	II	III	IV
1	105	114	108	109
2	112	113	Y	112
3	106	114	105	109

 

5(a) 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:

32(D)	33(E)	30(C)	28(B)	24(A)
51(C)	45(D)	41(A)	45(E)	29(B)
41 (E)	29 (A)	24 (B)	36 (D)	35 (C
38 (B	39(C)	42(E	23(A)	37(D)
38(A	24(B)	21(D)	29(C)	26(E)

Analyse the design with appropriate method and calculate the Critical Difference for the treatment mean yield

(b) 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

 

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