LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2010

ST 3504/ST 3502/ST 4500 – BASIC SAMPLING THEORY

 

 

 

Date : 02-11-10                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

 

ANSWER ALL QUESTIONS.                                                                                       (10 X 2 =20 marks)

 

1. What is meant by “Probability Sampling Design”?
2. Give an example of a “Statistic”.
3. What are the values of second order inclusion probabilities in simple random sampling without replacement when N=10 and n=3?
4. Show that the variance of sample mean under simple random sampling with replacement is greater than its variance under simple random sampling without replacement.
5. Under what condition PPSWR reduces to SRSWR?
6. Suggest an unbiased estimator for population total under PPSWR.
7. When do you recommend stratified random sampling?
8. Suggest an unbiased estimator of population mean in stratified random sampling.
9. List all possible circular systematic samples of size 3 when the population size is 10.
10. What is the probability of selecting a sample consisting of 3^rd and 4^th population units in LSS when N=12 and n=4?

            SECTION – B

 

ANSWER ANY FIVE QUESTIONS                                                                                (5 X 8 =40 marks)

 

11. Compare sampling and census.
12. Explain the terms : (i) Unbiasedness (ii) Variance (iii) Mean square error and (iv) Bias.
13. Show that under simple random sampling when N=3 and n=2 the estimator

is unbiased for the population mean and obtain its variance.

 

14. Explain Cumulative total method of PPS selection with an example.
15. Compare the efficiencies of under optimum and proportional allocation.
16. Explain proportional allocation for a given sample. Derive the variance of under proportional allocation.
17. Derive in terms of .
18. Compare the variances of sample mean under LSS and SRS in the presence of linear trend.

 

SECTION  – C

 

 

ANSWER ANY TWO QUESTIONS                                                                     (2 X 20 = 40 marks)

 

19. a) Establish the relationship between Bias, Variance and Mean Square error.
20. b) Illustrate with an example that unbiasedness of an estimator is design dependent.
21. a) Explain Lahiri’s method of PPS selection with proof.
22. b) Derive the variance of Hansen Hurwitz estimator under PPSWR and develop its unbiased

estimator.

21. a) A sampler has two strata with relative sizes  and  .  He believes that

and  can be taken as equal. For a given cost , assuming the stratum

sizes are large, show that

 

1. Derive the formula for Optimum allocation.

 

22. Write short notes on the following:
23. Balanced systematic sampling
24. Yates corrected estimator
25. Neyman allocation
26. Formation of Strata.

 

 

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