# IGNOU MST-005 Solved Assignment 2022

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## IGNOU MST-005 Solved Assignment 2022

MST-005 Solved Assignment is an e-book for students who want to specialise in statistics. This completed assignment will allow them to assess their degree of preparation and will be extremely beneficial. All questions and concerns have been addressed and clarified. As a result, students will comprehend the concepts of any question in the assignment.

 Assignment Paper IGNOU MST-005 Solved Assignment 2022 Subject Name Statistical Techniques No.of Pages in Solution 29 Course PGDAST Language ENGLISH Session 2022 Last Date for Submission of Assignment For June Examination 31st March 2022 or as per dates given in the Ignou website For December Examination 30th September 2022 or as per dates given in the Ignou website

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## IGNOU MST-005 Sample Solution 2022

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## IGNOU MST-005 Solved Assignment 2022

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## (Statistical Techniques)

MST-005: Statistical Techniques

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

(a)  The total number of all possible samples of size 2 without replacement from a population of size 7 is 21.

(b)  Consecutive 3 random numbers starting from 8937 by ‘middle square method’ are 8937, 8699, 6726.

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

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

(e)  In a big hall, there are 50 rows and each row has 60 students. A research scholar selects 10 rows randomly and then randomly selects 15 students from each selected row. It is an example of cluster sampling procedure.

2. (a) Draw all possible samples of size 2 from the population [2, 3, 4] and verify that ​$$E\left(\overline{x}\right)=\overline{X}$$​.Also find variance of ​$$\overline{x}$$

(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:

 Villages Stratum sizes (Ni) Means (xi) Standard deviations Village A 400 60 20 Village B 200 120 80

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

3. To determine the yield rate of wheat in a district of Punjab, 6 groups of 6 plots each were constructed. The data are 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 above data and find its sample mean. Further, explain the procedure of two-stage sampling if we want to draw a sample of 6 plots. Which are the 6 plots in your sample?

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?

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.

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

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

7. Identify the design given in the following table and then carry out the analysis:

 Column Row I II III IV I A8 C18 B11 D8 II C16 B10 D7 A4 III B12 D10 A6 C20 IV D10 A9 C28 B16

8. (a) The distribution function of Pareto distribution is given by ​$$f\left( x\right) =1-\left( \dfrac{k}{x}\right)^{a}:a >0,0 <k\leq x$$

Given a U~ U(0, 1), generate a random number from the above distribution, when a = 2 and k = 1. Suppose U = 0.5, then find x.

(b) Generate a complete cycle for the LCG given below: xi = (5xi−1 + 3)mod16, with xo= 5. A man tosses an unbiased coin ten times. Using the first ten random numbers generated above, obtain a sequence of heads and tails by taking Head (H) as u ≥ 0-5.

9.Times between successive crashes of a computer system were generated for a 6-month period and are given in increasing order as follows (time in hours):

 1 10 20 30 40 52 63 70 80 90 100 102 130 140 190 210 266 310 530 590 640 1340

The parameter a = 0.00435, mean = 1/α = 230 hrs.
Use the Kolmogorov-Smirnov test to examine the goodness of fit of exponential distribution.

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