LOYOLA COLLEGE (AUTONOMOUS), CHENNAI-600 034.

M.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2003

**ST 1802/ S 717 SAMPLING THEORY**

08.04.2003

1.00 – 4.00** **Max: 100 Marks

# SECTION – A (10 ´ 2 = 20 Marks)

## Answer ALL the questions. Each carries two marks

- Let the sampling design be

### If N=3 then what is the value of p_{68}?

- Given a fixed size sampling design yielding sample of size 5, what is the value

of ?

- Under what condition the mean square error of an estimator becomes its variance?
- List all possible balanced systematic samples of size 4 when N = 12.
- Under usual notations order V
_{SRS}, V_{SYS},V_{STR}assuming the presence of linear trend. - Name any two methods of PPS selection.
- When N=16 and n = 4, what will be your choice for random group sizes in random group method? Give reason.
- Define ratio estimator for the population total.
- Name any two randomised response techniques.
- Explain the term: Optimum allocation.

**SECTION ****–**** B** (5 ´ 8 = 40 Marks)

*Answer any FIVE. Each carries eight marks.*

- Show that under SRS,

where

- Explain any one method of PPS selection in detail with a supportive example.
- Show that under balanced systematic sampling, the expansion estimator coincides with the population total in the presence of linear trend.
- Derive the mean square error of and obtain the condition under which is more

efficient than .

- Explain the usefulness of two phase sampling in pps sampling.
- Describe in detail any one method of Randomised Response technique.
- Derive under Neyman allocation.
- Verify the following relations with an example

(Proof should not be given)

**Section ****–**** C**** ** (2 ´ 20 =20 Marks)

*Answer any TWO questions. Each carries twenty marks*.

- Describe random group method. Suggest an unbiased estimator for the

population total and derive its variance.

- Derive the first and second order inclusion probabilities in Midzeno sampling and

show that the Yates-Grundy estimator is nonnegative

- Develop Yates-corrected estimator.
- (a) Describe how double sampling is employed in ratio estimation (10)

(b) Write a descriptive note on two stage sampling. (10)