Download LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
THIRD SEMESTER – November 2008
ST 3502 / 4500 - BASIC SAMPLING THEORY
Date : 08-11-08
Time : 9:00 - 12:00
Dept. No.
BA 09
Max. : 100 Marks
PART A
Answer ALL the Questions.
(10 x 2 =20)
1. Define the term “statistic” in finite population sampling.
2. What do you mean by probability sampling?
3. What will happen to the variance of sample mean under simple random sampling without
replacement, if the sample size is increased?
4. Mention an unbiased estimator of V ( y ) in simple random sampling without replacement where y is
the sample mean.
5. Under what condition PPSWR reduces to SRSWR?
6. Give an unbiased estimator of the population total in PPSWR, when the sample size is one.
7. What is meant by Neyman allocation?
8. Under what condition Neyman allocation reduces to Proportional allocation?
9. Write all possible Circular systematic samples of size 3 when the population size is 7.
10. Write the down the model used for representing populations exhibiting linear trend in Sampling
Theory
PART B
Answer any FIVE Questions.
(5 x 8 =40)
11. Compare Sampling with Census.
12. Illustrate with an example thatUnbiasedness is a sampling design dependent property.
13. Derive V ( y ) under simple random sampling without replacement.
14. Define Hansen - Hurwitz estimator and obtain its variance under PPSWR.
15. Show that Lahiri’s method of sample selection is a PPS selection method.
16. Derive the formula for Optimum allocation for fixed variance in stratified random sampling.
17. Explain Balanced systematic sampling and derive the V ( y ) under BSS assuming the population
values possess linear trend
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18. Derive the condition under which LSS is more efficient than SRS in terms of S wsy
PART C
Answer any TWO Questions.
(2 x 20 =40)
19. (a) Bring out the relationship between Mean Square Error, Bias and Variance of an estimator
(b) Show that s 2 is unbiased for S 2 in SRSWOR
20. Assume that there are two strata with S1  S 2 and relative weights W1 and W2 . Show that for the
V prop
W1c1  W2 c 2

given cost C  c1n1  c2 n2 ,
. Assume the strata sizes are large.
2
Vopt
W1 c1  W2 c 2
21. Derive the Yates corrected estimator under Linear Systematic Sampling for populations possessing
linear trend.
22. Write short notes on the following
(a) Cumulative Total Method
(b) Modified Systematic Sampling
(c) Proportional allocation
(d) Limitations of Systematic Sampling
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