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IGNOU MST 5 SOLVED ASSIGNMENT 2024

IGNOU MST 5 SOLVED ASSIGNMENT 2024


IGNOU MST 5 Solved Assignment 2024
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IGNOU MST 5 Solved Assignment 2024

This is latest Solved Assignment of MST 5 of PGDAST . 

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Last Date of Submission of IGNOU MST-05 (PGDAST) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Semester Wise
January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam).
July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).

Title NameIGNOU MST 5 Solved Assignment 2024
TypeSoft Copy (E-Assignment) .pdf
UniversityIGNOU
DegreePG DIPLOMA PROGRAMMES
Course CodePGDAST
Course NamePost Graduate Diploma in Applied Statistics
Subject CodeMST 5
Subject NameTUTOR MARKED ASSIGNMENT
Year2024
Session
LanguageEnglish Medium
Assignment CodeMST-05/Assignmentt-1//2024
Product DescriptionAssignment of PGDAST (Post Graduate Diploma in Applied Statistics) 2024. Latest MST 05 2024 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission
Last Date of Submission of IGNOU MST-05 (PGDAST) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Semester Wise
January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam).
July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).

Rs. 400
Rs. 205
Questions Included in this Help Book

Ques 1.

State whether the following statements are true or false and also give the reason in support of your answer.
c) In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn
.d) One-way analysis of variance is a generalization of the two sample t-test.
e) If experimental error is reduced considerably and the efficiency of the design is
decreased.
f) If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.
g) If one wants to convert random numbers selected from two digit numbers 00-99 to
uniformly distributed U (0, 1) variables then one has to divide them by 99.

Ques 2.

Assume that you have to perform a sample survey for Family expenditure of the faculty of Indira Gandhi National Open University. Then explain the main steps involved in the planning and execution of that sample survey.

Ques 3.

In a class of Statistics, total number of students is 30. Select the linear and circulur systematic random samples of 10 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            

Ques 4.

To determine the yield rate of wheat in a district of Punjab, 6 groups were constructed of 6 plots each. The data is given in the following table:

Plot No Group 1 Group 2 Group 3 Group 4 Group 5 Group 6
1 8 6 18 13 17 12
2 13 5 8 7 15 15
3 11 16 6 13 10 11
4 26 5 10 6 21 17
5 13 16 16 7 20 8
6 31 5 20 2 25 10

Select a cluster sample of 3 clusters from the given data and find sample mean.

Ques 5.

Three varieties A, B and C of wheat are shown in five plots each of the following fields per acre as obtained:

Plots A B C
1 8 7 12
2 10 5 9
3 7 10 13
4 14 9 12
5 11 9 14

Set up a table of analysis of variance and find out whether there is significant difference between the fields of these varieties.

Ques 6.

An experiment was planned to study the effect of Sulphate, Potash and Super Phosphate on the yield of potatoes. All the combinations of 2 levels of Super Phosphate [0 cent (p0) and 5 cent (p1)/ acre] and two levels of Sulphate and Potash [0 cent (k0) and 5 cent (k1)/acre] were studied in a randomised block design with 4 replications each. The (1/70) yields [lb per plot = (1/70) acre] obtained are given in table below:

Blocks Yields (lbs per plot)
I (1)
23

k

25

p

22

kp

38
II

p

40

 (1)
26

k

36

kp

38
III (1)
29

k

20

pk

30

p

20
IV

kp

34

k

31

p

24

 (1)
28

 Analyse the data and give your conclusions.

Ques 7.

By generating 10 uniform random variate U (0, 1) estimate the integral

\theta = \frac{1}{\sqrt{2\pi}}\int_{-1}^{2}e^{\frac{-x^2}{2}} dx

Recognizing this function as probability density function of N (0, 1), compare the value of \widehat{\theta} with \theta.

Ques 8.

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

Village N_i  \overline{X_i} S_i^2
Collage A 400 60 20
Collage B 200 120 80

 Find the number of 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 that of SRSWOR.

Ques 9.

A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the results are shown in the following table:

Machine First shift Second Shift
M T W Th F M T W Th F
A 6 4 5 5 4 5 7 4 6 8
B 10 8 7 7 9 7 9 12 8 8
C 7 5 6 5 9 9 7 5 4 6
D 8 4 6 5 5 5 7 9 7 10

 Perform an analysis of variance to determine at 5% level of significance, whether there is a difference (a) Between the machines and (b) Between the shifts.

Ques 10.

In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn .

Ques 11.

One-way analysis of variance is a generalization of the two sample t-test.

Ques 12.

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

Ques 13.

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

Ques 14.

If one wants to convert random numbers selected from two digit numbers 00-99 to uniformly distributed U (0, 1) variables then one has to divide them by 99.

Ques 15.

Assume that you have to perform a sample survey for Family expenditure of the faculty of Indira Gandhi National Open University. Then explain the main steps involved in the planning and execution of that sample survey.

Ques 16.

In a class of Statistics, total number of students is 30. Select the linear and circulur systematic random samples of 10 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                

 

Ques 17.

To determine the yield rate of wheat in a district of Punjab, 6 groups were constructed of 6 plots each. The data is given in the following table: 

Plot No. Group 1 Group 2 Group 3 Group 4 Group 5 Group 6
1 8 6 18 13 17 12
2 13 5 8 7 15 15
3 11 16 6 13 10 11
4 26 5 10 6 21 17
5 13 16 16 7 20 8
6 31 5 20 2 25 10

Select a cluster sample of 3 clusters from the given data and find sample mean.

Ques 18.

Three varieties A, B and C of wheat are shown in five plots each of the following fields per acre as obtained:

Plots A B C
1 8 7 12
2 10 5 9
3 7 10 13
4 14 9 12
5 11 9 14

Set up a table of analysis of variance and find out whether there is significant difference between the fields of these varieties.

Ques 19.

An experiment was planned to study the effect of Sulphate, Potash and Super Phosphate on the yield of potatoes. All the combinations of 2 levels of Super Phosphate [0 cent (p0) and 5 cent (p1)/ acre] and two levels of Sulphate and Potash [0 cent (k0) and 5 cent (k1)/acre] were studied in a randomised block design with 4 replications each. The (1/70) yields [lb per plot = (1/70) acre] obtained are given in table below: 

Blocks Yields (lbs per plot)
I

(1)

23

k

25

p

22

kp

38
II

p

40

(1)

26

k

36

kp

38
III

(1)

29

k

20

pk

30

p

20
IV

kp

34

k

31

p

24

(1)

28

Analyse the data and give your conclusions.

Ques 20.

By generating 10 uniform random variate U (0, 1) estimate the integral

\theta =\frac{1}{\sqrt{2\pi }}\int_{-1}^{2}e^{-x^{2}/2}dx

Recognizing this function as probability density function of N (0, 1), compare the value of \theta with \theta.

Ques 21.

A sample of 100 villagers is to be drawn from a population of villages 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

Find the number of 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 that of SRSWOR.

Ques 22.

A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the results are shown in the following table: 

Machine First shift Second Shif
M T W Th F M T W Th F
A 6 4 5 5 4 5 7 4 6 8
B 10 8 7 7 9 7 9 12 8 8
C 7 5 6 5 9 9 7 5 4 6
D 8 4 6 5 5 5 7 9 7 10

Perform an analysis of variance to determine at 5% level of significance, whether there is a difference (a) Between the machines and (b) Between the shifts.

Ques 23.

In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn .

Ques 24.

One-way analysis of variance is a generalization of the two sample t-test.

Ques 25.

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

Ques 26.

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

Ques 27.

If one wants to convert random numbers selected from two digit numbers 00-99 to uniformly distributed U (0, 1) variables then one has to divide them by 99.

Ques 28.

Assume that you have to perform a sample survey for Family expenditure of the faculty of Indira Gandhi National Open University. Then explain the main steps involved in the planning and execution of that sample survey.

Ques 29.

In a class of Statistics, total number of students is 30. Select the linear and circulur systematic random samples of 10 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                

b) To determine the yield rate of wheat in a district of Punjab, 6 groups were constructed of 6 plots each. The data is given in the following table:

Plot No. Group 1 Group 2 Group 3 Group 4 Group 5 Group 6
    1     8     6    18    13 17    12
    2    13     5    8    7 15    15
    3    11    16    6   13 10    11
    4    26     5    10    6 21    17
    5    13    16    16    7 20    8
    6    31     5    20    2 25    10

Select a cluster sample of 3 clusters from the given data and find sample mean.

Ques 30.

Three varieties A, B and C of wheat are shown in five plots each of the following fields per acre as obtained:

Plots A B C
1 8 7 12
2 10 5 9
3 7 10 13
4 14 9 12
5 11 9 14

Set up a table of analysis of variance and find out whether there is significant difference between the fields of these varieties.

Ques 31.

An experiment was planned to study the effect of Sulphate, Potash and Super Phosphate on the yield of potatoes. All the combinations of 2 levels of Super Phosphate [0 cen \left ( P0 \right ) and 5 cent \left ( P1 \right ) \left ( P1 \right )/ acre] and two levels of Sulphate and Potash [0 cen \left ( K0 \right ) and 5 cent \left ( K0 \right )/ acre]  were studied in a randomised block design with 4 replications each. The (1/70) yields [lb per plot = (1/70) acre] obtained are given in table below: 

Blocks Yields
       
                    I

(1)

23

k

25

p

22

kp

38
                   II

p

40

(1)

26

k

36

kp

38
                   III

(1)

29

k

20`

pk

30

p

20
                    IV

kp

34

k

31

p

24

(1)

28

Analyse the data and give your conclusions.

Ques 32.

By generating 10 uniform random variate U (0, 1) estimate the integral\Theta =\frac{1}{\sqrt{2\pi }}\int_{-1}^{2}e^{-x^{2/2}}dx

Recognizing this function as probability density function of N (0,1), compare the value of \theta ^{^} with \theta ^{^}.

Ques 33.

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

Village N_{1} \bar{X}_{1} {S}_{1}^{2}
Collage A 400. 60 20
Collage B 200 120 80

Find the number of 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 that of SRSWOR.

Ques 34.

A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the results are shown in the following table:

Machine  First Shift  Second Shift
                   
A 6 4 5 5 4 5 7 4 6 8
B 10 8 7 7 9 7 9 12 8 8
C 7 5 6 5 9 9 7 5 4 6
D 8 4 6 5 5 5 7 9 7 10

Perform an analysis of variance to determine at 5% level of significance, whether there is a difference (a) Between the machines and (b) Between the shifts.

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Course Name Post Graduate Diploma in Applied Statistics
Course Code PGDAST
Programm PG DIPLOMA PROGRAMMES Courses
Language English

 

 

 
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