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~:CTFr~ Time Allowed: Three Hours

_STATISTICS (Paper II)

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~3fcn: 250

Maximum Marks : 250

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QUESTION PAPER SPECIFIC INSTRUCTIONS

Please read each of the following instructions carefully before attempting questions.

There are EIGHT questions divided into two SECTIONS and printed both in HINDI and in ENGLISH.

Candidate has to attempt FIVE questions in all.

Question No. 1 and 5 are compulsory and out of the remaining, TIIREE are to be attempted choosing at least ONE from each section.

The number of marks carried by a question/part is indicated against it.

Answers must be written in the medium authorized in the Admission certificate which must be stated clearly on the cover of this Question-cum-Answer (QCA) booklet in the space provided. No marks will be given for answers written in medium other than the authorized one.

Wherever any assumptions are made for answering a question, they must be clearly indicated.

Charts/Figures, wherever required, shall be drawn in the space provided for answering the question itself.

Attempts of questions shall be counted in chronological order. Unless struck off, attempt of a question shall be counted even if attempted partly. Any page or portion of the page left blank in the answer book must be clearly struck off.

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30

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5.(a)

5.(b)

5.(c)

5.(d)

5.(e)

6.(a)

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6.(c)

7.(a)

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8.(a)

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SECTION 'A' 1.(a) What is meant by Statistical Quality Control (SQC) ? What is its main purpose ?

Give its uses. Also mention different tools for SQC. 10

1.(b) What are the different methods for determining Reliability ? Explain any two of them and also give their merits and demerits. 10

1.(c) Explain different steps in the preparation of Control Charts. IO

1.(d) Give any three definitions of Operations Research. What are the advantages and disadvantages of operations research models ? 10

1.(e) What is Linear Programming ? Give its advantages and limitations. 10

2.(a) Explain Double sampling Plan and develop expression· required for drawing OC curve in Double sampling Plan. 15

2.(b) Explain the procedure for drawing the 5-points A S N curve for the sequential sampling plan. 15

2.(c) In welding of seams, number of defects that were identified in one seam each hour are given below:

2-1-2013

6 am 7 am 8 am 9 am 10 am 11 am 12 noon I pm 2 pm 3 pm 4 pm 5 pm 6 pm

2 4 7 3 I 4 8 9 5 3 7 11 6

3-1-2013

6 am 7 am 8 am 9 am IO am 11 am 12 noon lpm 3 pm 4 pm 5 pm

4 9 9 6 4 3 9 7 4 7 12

Draw the control chart for number of defects and give your conGlusion. 20

3.(a) Four counters are being opened on the frontier of a country to check the passports and necessary papers of the tourists . The tourists choose the counter at random. If the arrivals at the frontier are Poisson at the rate A and the service time is exponential with parameters .A/2, what is the steady state average queue at each counter? 10

3.(b) Solve the following game problem graphically: 10

Player B ---7 I II Ill IV Player A.t

I 8 5 - 7 9

II - 6 6 4 - 2

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3.( c) A cement factory manager is considering the least way to transport cement from his three factories A, B and C to depots P, Q, R and S. The weekly production and demands along with transportation costs are given below. What should be the distribution programme ? 30

Factory Depot P Depot Q Depot R Depot S Production

A 10 8 7 12 500

B 12 15 6 10 500

c 8 10 12 14 900

demand 700 550 450 300

4.(a) A truck owner finds from his past records that the maintenance cost of a truck (whose purchase price is Rs. 30,00,000) during the first 8 years of its life and the resale price at the end of each year is as follows :

Year 1 2 3 4 5 6 7 8

Maintenance Cost (Rs. ) 360000 480000 600000 720000 840000 960000 1080000 1200000

Resale Price (Rs.) 2000000 1500000 1000000 800000 700000 600000 500000 400000

In which year is the replacement due? 10

4.(b) What is Assignment Problem ? With usual notation give its mathematical formu-lation. Compare this with Mathematical form of Transportation Model. 10

4.( c) Solve the following LPP :

5.(a)

S.(b)

Maximise Z = 8x 1 - 4.xz Subject to 4x 1 + 5x2 ~ 20 -x1 + 3x2 =:: -23

where x 1 =:: 0 and x2 is unrestricted in sign.

SECTION 'B'

Define Time Series. Write its components and explain them.

What are the different measures of Mortality ? Explain briefly.

30

10

10

5.(c) What is cost of living index numbers? Mention the main steps in the construction of cost of living Index. What are its uses ? 10

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S.(d) What is Validity of Test Scores? How you will calculate Validity? Also make comparison with the concept of reliability. 10

S.(e) What are Hospital Statistics? How they are useful? 10

6.(a) Complete the following Table : 25

Age in lx dx qx Px Lx TX Eo x years

11 12000 ? ? ? ? ? ?

12 8000 ? ? ? ? ? ?

13 6000 ? ? ? ? ? ?

14 4000 3000 ? ?

6.(b) Explain the Logistic growth curve for the population growth. Give any two methods of fitting the Logistic Growth Curve. 15

6.(c) What is the problem of multicollinearity? What are its consequences? 10

7.(a) Briefly explain the Schematic representation of the BOX-JENKINS methodology for time series modelling. 20

7.(b) Explain any three main sources of demographic data mentioning their limitations and uses. 15

7.(c) Write briefly on methods of collecting Agricultural Statistics m India. Also mention its shortcomings. 15

8.(a) Clearly explain the following fertility rates .and also give their advantages and disadvantages :

(i) Crude Birth Rate (ii) General Fertility Rate and (iii) Age Specific Fertility Rates 15

8.(b) Explain how Fertility can be estimated as an application of Stable Population Theory. 10

8.(c) Show · that Marshall-Edgeworth Index number lies between Laspeyre's and Paasche's Index numbers. 10

8.(d) What is CSO ? Explain and mention its main functions. 15

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