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Unformatted text preview: 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 SECTION − A Answer ALL the questions. Each carries TWO marks 01. Let the sampling design be 1 P( s ) = 10c3 0 if n( s ) = 3 Max: 100 Marks (10 × 2 = 20 Marks) otherwise If N=3 then what is the value of π68? 02. Given a fixed size sampling design yielding sample of size 5, what is the value of 03. 04. 05. 06. 07. ∑π 2 j ? =
j1 N Under what condition the mean square error of an estimator becomes its variance? List all possible balanced systematic samples of size 4 when N = 12. Under usual notations order VSRS, VSYS,VSTR assuming the presence of linear trend. Name any two methods of PPS selection. When N=16 and n = 4, what will be your choice for random group sizes in random group method? Give reason. 08. Define ratio estimator for the population total. 09. Name any two randomised response techniques. 10. Explain the term: Optimum allocation. SECTION − B Answer any FIVE. Each carries eight marks. 11. Show that under SRS, ˆ ν ( y SRS ) = N 2 N −n 1 ˆ ∑ yi − y Nn n − 1 i ∈s (5 × 8 = 40 Marks) ( ) 2 1 ˆ where y = ∑ yi n i∈s 12. Explain any one method of PPS selection in detail with a supportive example. ˆ 13. Show that under balanced systematic sampling, the expansion estimator y BSS coincides with the population total in the presence of linear trend. ˆ ˆ 14. Derive the mean square error of YR and obtain the condition under which YR is more efficient than Y . ˆ 15. Explain the usefulness of two phase sampling in pps sampling. 16. Describe in detail any one method of Randomised Response technique. ˆ 17. Derive V Y under Neyman allocation. ()
STR 18. Verify the following relations with an example (1) ∑π
≠i N ij = (n − 1)π i (2) ∑π
1≡1 N i =n (Proof should not be given) SECTION − C Answer any TWO questions. Each carries twenty marks. (2 × 20 =20 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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This note was uploaded on 03/13/2010 for the course STATISTIC 472 taught by Professor Amjad during the Spring '08 term at Yarmouk University.
- Spring '08