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ignou MST 5 solved 2024

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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 Name	ignou MST 5 solved assignment 2024
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	PG DIPLOMA PROGRAMMES
Course Code	PGDAST
Course Name	Post Graduate Diploma in Applied Statistics
Subject Code	MST 5
Subject Name	TUTOR MARKED ASSIGNMENT
Year	2024
Session	-
Language	English Medium
Assignment Code	MST-05/Assignmentt-1//2024
Product Description	Assignment 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).
Assignment Code	MST 5/2024

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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)

(1)
23

(1)
26

III

(1)
29

(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
Machine	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.

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.

Blocks

Yields (lbs per plot)

(1)

III

(1)

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

Ques 22.

Machine	First shift					Second Shif
Machine	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.

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

(1)

III

(1)

20`

(1)

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

Ques 34.

Machine	First Shift	Second Shift
Machine
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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Rs. 50