M.Sc. (Semester II) (CBCS) Examination Oct/Nov-2017
Statistics
SAMPLING THEORY
Day Date: Monday, 27-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: Q.1 and Q.2 are compulsory.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Attempt five questions.
Q.1 Select the correct alternative: 05
300 units of a population are divided into two strata with N1 100, N2
200, S1 2 and S2 3. If 20 units of a sample have to be selected by
Neyman allocation, The two sample sizes from strata will be

12)
15)
Precision of random sample
Decreases with the increase
in the sample size
Increases with the increase in
the sample size
Has no relation with the size
of the sample.
None of these
A sample survey is to be conducted to estimate the average size of
land holding of households in a district. Then which one of the following
will be the most appropriate procedure of sampling
Simple random sampling Stratified random sampling
Systematic sampling Multistage sampling
A simple random sample of 10 units is drawn without replacement from
a serially numbered population of 100 units. The probability that U1 and
U2 both in the sample is
0
1
10

1
100

1
110
Consider a population having units 1 and draw a sample of
size 2 from it. The standard error of sample mean in case of
without replacement is
0.6 0.75
1 0.85
Fill in the blanks: 05
Deming's technique deals with
When n units are selected with SRSWR, the total numbers of possible
samples are
The probability of inclusion of ith and jth unit in the sample is called

For proportional allocation, ni
Non-response errors introduce in the estimator.
Page 2 of 2
SLR-MS-653
State true and false 04
Regression estimator is always better than the sample mean under
SRSWOR.
Sampling error decreases as the sample size increases.
SRSWOR scheme is always more precise than SRSWR scheme for a
given sample size.
In stratified sampling, the strata are constructed such that they are
among homogeneous.
Q.2 Answer the following:- 06
Describe the method of cluster sampling.
Distinguish between sampling error and non-sampling error.
Write short notes on the following: 08
Midzuno system of sampling
Deep stratification
Q.3 Explain the concept of systematic sampling. Derive the sampling variance of
unbiased estimator of a population mean under the linear systematic
sampling.
07
Describe simple random sampling. In SRSWOR, show that the probability of
drawing a specified unit at every draw is the same.
07
Q.4 Define Horvitz-Thompson estimator for population total in PPSWOR
sampling. Derive its expected value and sampling variance.
07
Explain various sample allocation criteria in stratified sampling. 07
Q.5 In SRSWOR of n clusters each containing M elements from a population of
N clusters. Obtain mean and variance of estimator of sample mean.
07
Describe Hansen-Hurwitz technique for dealing with non-response in postal
surveys.
07
Q.6 Outline ratio method of estimation. In SRSWOR, derive bias of the estimator. 07
Define two stage sampling design and give a practical situation where such
a design is used.
07
Q.7 Explain regression method for estimation of population mean. Assuming
SRSWOR, derive MSE of the estimator.
07
Develop Des Raj ordered estimator of population mean based on sample
size 2. Show that it is unbiased.