LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

BA 09

THIRD SEMESTER – November 2008

ST 3502 / 4500 – BASIC SAMPLING THEORY

 

 

 

Date : 08-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

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 in simple random sampling without replacement where 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)

 

1. Compare Sampling with Census.
2. Illustrate with an example thatUnbiasedness is a sampling design dependent property.
3. Derive under simple random sampling without replacement.
4. Define Hansen – Hurwitz estimator and obtain its variance under PPSWR.
5. Show that Lahiri’s method of sample selection is a PPS selection method.
6. Derive the formula for Optimum allocation for fixed variance in stratified random sampling.
7. Explain Balanced systematic sampling and derive the under BSS assuming the population values possess linear trend
8. Derive the condition under which LSS is more efficient than SRS in terms of

 

PART C

Answer any TWO Questions.                                                                (2 x 20 =40)

 

1. (a) Bring out the relationship between Mean Square Error, Bias and Variance of an estimator

(b) Show that is unbiased for in SRSWOR

1. Assume that there are two strata with and relative weights and . Show that for the given cost , . Assume the strata sizes are large.
2. Derive the Yates corrected estimator under Linear Systematic Sampling for populations possessing linear trend.
3. Write short notes on the following

• Cumulative Total Method
• Modified Systematic Sampling
• Proportional allocation
• Limitations of Systematic Sampling

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