LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
THIRD SEMESTER – APRIL 2012
ST 3504/ST 3502/ST 4500 – BASIC SAMPLING THEORY
Date : 26-04-2012 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PART – A
Answer ALL the questions: (10×2= 20 Marks)
- Define Population and sample.
- Explain sampling frame and give an example.
- Define simple random sampling without replacement.
- Distinguish between a questionnaire and schedule.
- In SRSWOR, find the number of samples of size 3 that can be drawn from a population of size 15.
- Distinguish between bias and error.
- Explain stratified random sampling.
- What are the merits of stratified random sampling?
- Define linear systematic sampling.
- What is meant by circular sampling?
PART – B
Answer any FIVE questions : (5×8=40 Marks)
- Discuss briefly the basic principles of a sample survey.
- Explain Lottery Method and Random Number Table Method of unit selection.
- In SRSWOR, prove that the sample mean is unbiased estimator of population mean. Also find its variance.
- In SRSWR, prove that .
- Explain modified systematic sampling and derive the expression for variance of the sample mean.
- Explain the advantages and disadvantages of systematic sampling.
- Explain cumulative total method of PPS selection.
- In usual notations, prove that the systematic sample mean is more precise than the mean of SRSWOR if .
PART – C
Answer any TWO questions: (2×20=40 Marks)
- (a) Discuss the advantages of sampling over completer enumeration.
(b) A population contains 12 units with y-values arranged according to their labels as
3, 5, 4, 7, 8, 2, 9, 12, 11, 15, 13, 14. List all possible linear systematic samples of
size 4.
- (a) Derive the variance of Hansen-Hurwitz estimator for population total.
(b) Explain proportional allocation and optimum allocation.
- Prove that when we compare stratified random sampling with SRS .
- Compare simple random sampling and linear systematic sampling in the presence of linear trend.
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