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IGNOU MST-005 Solved Assignment 2024 | PGDAST

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

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IGNOU MST-005 Assignment Question Paper 2024

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

a) In SRWOR, the possible numbers of sample of size \(\mathrm{n}\) from a population of size \(\mathrm{N}\) if sampling is done with replacement is \(\mathrm{N}^{\mathrm{n}}\).

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

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) 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.

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.

3 a) 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:

\(\begin{array}{rrrrrrrrrrrrr}\text { Age: } & 22 & 25 & 22 & 21 & 22 & 25 & 24 & 23 & 22 & 21 & 20 & 21 \\ 22 & 23 & 25 & 23 & 24 & 22 & 24 & 2421 & 20 & 23 & 21 & 22 \\ 20 & 20 & 21 & 22 & 25 & & & & & & & & \end{array}\)

 

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 1Group 2Group 3Group 4Group 5Group 6
18618131712
2135871515
311166131011
42651062117
51316167208
63152022510

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

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

PlotsABC
18712
21059
371013
414912
511914

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

5. 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 \(\left[0\right.\) cent \(\left(\mathrm{p}_{0}\right)\) and 5 cent \(\left(\mathfrak{p}_{1}\right) /\) acre] and two levels of Sulphate and Potash [0 cent \(\left(\mathrm{k}_{0}\right)\) and 5 cent \(\left.\left(\mathrm{k}_{1}\right) / \mathrm{acre}\right]\) 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:

BlocksYields (lbs per plot)
I(1)kpkp
 23252238
IIp(1)kkp
 40263638
III(1)kpkp
 29203020
IVkpkp(1)
 34312428

Analyse the data and give your conclusions.

6. By generating 10 uniform random variate \(\mathrm{U}(0,1)\) estimate the integral

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

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

7. A sample of 100 villagers is to be drawn from a population of villages A and \(\mathrm{B}\). The population means and population mean squares of their monthly wages are given below:

VillageNiX¯iSi2
Collage A4006020
Collage B20012080

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. 8. A manufacturer wishes to determine the effectiveness of four types of machines \((\mathrm{A}, \mathrm{B}, \mathrm{C}\) 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:

MachineFirst shiftSecond Shift
MTWThFMTWThF 
A6455457468 
B108779791288 
C7565997546 
D84655579710

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.

\(sin\left(\theta -\phi \right)=sin\:\theta \:cos\:\phi -cos\:\theta \:sin\:\phi \)

MST-005 Sample Solution 2024

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IGNOU MST-005 Solved Assignment 2023
IGNOU MST-005 Solved Assignment 2023
IGNOU MST-005 Solved Assignment 2023
IGNOU MST-005 Solved Assignment 2023
IGNOU MST-005 Solved Assignment 2023

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\(cos\left(\theta +\phi \right)=cos\:\theta \:cos\:\phi -sin\:\theta \:sin\:\phi \)

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