LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

YB 13

THIRD SEMESTER – April 2009

ST 3502 / ST 4500 – BASIC SAMPLING THEORY

 

 

 

Date & Time: 02/05/2009 / 9:00 – 12:00   Dept. No.                                                   Max. : 100 Marks

 

 

PART A (10 x 2 = 20 Marks)

Answer All Questions:

1. Distinguish between census method and sampling procedure.
2. Define Sampling design and Probability Sampling.
3. What is simple random sampling?
4. Prove that SRSWOR sample mean is an unbiased estimate of the population mean.
5. Write down the two steps to select one unit by Lahiri’s method of PPS selection.
6. What is PPSWR sample?
7. Explain the need of stratified sampling.
8. What is proportional allocation?
9. What is circular systematic sampling?
10. What is a balanced systematic sampling scheme?

PART B (5 x 8 = 40 Marks)

Answer any Five Questions:

1. What are the advantages of sampling over census method? What are its limitations?
2. Under simple random sampling is unbiased for the population total and also obtain its variance.
3. Marks secured by over one lakh students in a competitive examination were displayed jin 39 display boards. In each board marks of approximately 3000 students were given. Kiran, a student who scored 94.86 marks wanted to know how many candidates have scored more than him. In order to estimate the number of student who have scored more than him, he took a SRS of 10 boards and counted the number of students in each board who have scored more than him. The following is the data collected.

14, 29, 7, 13, 0, 36, 11, 43, 27 and 5.

Estimate the number of student who would have scored more than Kiran and also estimate the variance of its estimate.

 

 

1. Prove that the probability of selecting the i^th unit in the first effective draw is , in Lahiri’s method of  PPS selection.
2. Derive the variance for Hansen – Hurwitz estimator.
3. Explain the procedure of optimum allocation of sample size.
4. Derive an unbiased estimator for the population total and its variance under proportional allocation.
5. Prove that , where  and  are the conventional expansion estimators under linear systematic sampling and simple random sampling respectively.

PART C (2 x 20 = 40 Marks)

Answer any two Questions:

1. (a) Prove that under SRS, S_xy.

(b) Derive average mean squared errors under balanced systematic and modified systematic sampling schemes and compare them.

1. (a) Derive an unbiased estimator for population total in PPS sample and also obtain its variance.

(b) Prove that in Stratified random sampling with given cost function of the form , is minimum if _.

1. If the population consists of a linear trend, then prove that .
2. (a) Obtain the relative efficiency of systematic sample as compared to simple random sampling without replacement.

(b) Describe Lahiri’s method of selection and its merits over cumulative method.

 

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