LOYOLA  COLLEGE (AUTONOMOUS), CHENNAI-600 034.

M.Sc. DEGREE  EXAMINATION  – STATISTICS

FIRST SEMESTER  – APRIL 2003

ST  1802/ S  717   SAMPLING  THEORY

08.04.2003

1.00 – 4.00                                                                                             Max: 100 Marks

SECTION – A                                (10 ´ 2 = 20 Marks)

Answer ALL the questions.  Each carries two marks

1. Let the sampling design be

 

               If N=3 then what is the value of p₆₈?

 

2. Given a fixed size sampling design yielding sample of size 5, what is the value

of ?

3. Under what condition the mean square error of an estimator becomes its variance?
4. List all possible balanced systematic samples of size 4 when N = 12.
5. Under usual notations order V_SRS, V_SYS,V_STR assuming the presence of linear trend.
6. Name any two methods of PPS selection.
7. When N=16 and n = 4, what will be your choice for random group sizes in random group method? Give reason.
8. Define ratio estimator for the population total.
9. Name any two randomised response techniques.
10. Explain the term: Optimum allocation.

 

SECTION  – B                                              (5 ´ 8 = 40 Marks)

Answer any FIVE.  Each carries eight marks.

11. Show that under SRS,

 

where

12. Explain any one method of PPS selection in detail with a supportive example.
13. Show that under balanced systematic sampling, the expansion estimator coincides with the population total in the presence of linear trend.
14. Derive the mean square error of and obtain the condition under which is more

efficient than .

 

 

 

 

 

15. Explain the usefulness of two phase sampling in pps sampling.
16. Describe in detail any one method of Randomised Response technique.
17. Derive under Neyman allocation.
18. Verify the following relations with an example

 

(Proof should not be given)

 

Section – C                                    (2 ´ 20 =20 Marks)

Answer any TWO questions.  Each carries twenty marks.

 

19. Describe random group method. Suggest an unbiased estimator for the

population total and derive its variance.

20. Derive the first and second order inclusion probabilities in Midzeno sampling and

show that the Yates-Grundy estimator is nonnegative

21. Develop Yates-corrected estimator.
22. (a)  Describe how double sampling is employed in ratio estimation              (10)

 

(b)  Write a descriptive note on two stage sampling.                                     (10)

 

 

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