LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

           B.Sc. DEGREE EXAMINATION – STATISTICS

NO 13

THIRD SEMESTER – APRIL 2008

ST 3502/ 4500 – BASIC SAMPLING THEORY

 

 

 

Date : 29-04-08                  Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL questions:                                                       (10×2=20)

1. In what situations sampling is inevitable?
2. How would you distinguish between estimate and estimator?
3. Differentiate between SRSWR and SRSWOR.
4. Define standard error of an estimator.
5. Explain pps sampling.
6. Explain cumulative total method of selecting pps sampling.
7. What do you understand by stratified random sampling?
8. Distinguish between systematic sampling and stratified random sampling.
9. What is circular systematic sampling?
10. What are the advantages of systematic sampling?

 

SECTION-B

Answer any FIVE questions:                                                           (5×8=40)

1. Explain the principles of sampling methods.
2. In SRSWOR, prove that sample mean is an unbiased estimator of the population mean and its sampling variance is given by .
3. Explain the various types of allocations used in stratified random sampling method.
4. Find the relative precision of systematic sample mean with simple random sample mean.
5. A village has 10 holdings consisting of 50, 30, 45, 25, 40, 26, 24, 35, 28 and 27 fields. Select a sample of size 4 by using Lahiri’s method.
6. Explain sampling and non sampling errors.
7. Derive the formulae for the mean and variance of systematic sample..
8. Distinguish between probability and non-probability sampling and write down their advantages and disadvantages.

 

SECTION – C

Answer any TWO questions:                                                           (2×20=40)

1. a) Describe Lahiri’s method of selection and it’s merits over cumulative method.

1. b) A random sample of size n=2 was drawn from a colony of 5 households having monthly income as follows:

Household:      1          2          3          4          5

Income(Rs):    156      149      166      164      155

• Calculate population mean and population variance .
• Enumerate all possible samples of size 2 by the replacement method and show that the sample mean gives an unbiased estimate of the population mean and find its sampling.

Variance: Also show that s² is an unbiased estimate of the population variance .

1. a) Show that under fixed cost.

1. b) Compare the variances of the sample mean under systematic sample with stratified and simple random sampling, assuming linear trend.

1. a) Explain different systematic sampling schemes.

1. b) Derive the variance of Hansen-Hurwitz estimator for population total.

1. a) Show that in SRSWOR the probability of selecting a sample of size ‘n’ from ‘N’ units is 1/Ncn.

1. b) In a bank there are 5000 deposit accounts. A random sample of 50 accounts was drawn WOR and the following information was obtained and . Where Y_i denotes the amount in a deposit account. Find an unbiased estimate of the average amount in a deposit account and find its estimated variance.

 

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