M.Sc. (Statistics)(Semester II) (CBCS) Examination, 2017
Sampling Theory
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Day Date: Saturday, 29-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
N.B. Attempt five questions.
Q.no.1 and Q.2 are compulsory.
Attempt any three from Q.3 to Q.7
Figures to the right indicate full marks.
Q.1 Choose the correct alternatives. 05
1g) A population of size N=5 units has mean and S2=100
A simple random of size n=2 units is drawn without replacement
and sample mean is denoted by Then
144 174 50 30
2 In systematic sample of size n from a population of size
where k is given, the probability that a specified unit is included in
the sample is




3 A large city is subdivided into 150 non-overlapping blocks. Five
blocks are selected at random and completely enumerated. This
procedure is known as
Systematic sampling Cluster sampling
Stratified sampling Partial census
4 The regression estimator is appropriate in a situation

Regression of Yon X is linear and line passes through origin
Regression of Y on X is linear and line does not passes
through origin.
Regression of Y on X is non-linear and passes through origin.
Regression of Y on X in non-linear and does not passes
through origin.
In simple random sampling without replacement, the probability
that a particular unit will be selected at rth draw is




Fill in the blanks. 05
1 In Midzuno sampling scheme, the unit at first draw is selected with

2 In simple random sampling, bias of ratio estimator is
3 Cluster sampling is good alternative when is not available.
4 The probability of including the unit i in the sample is
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5 Variance of proportional allocation is always than that of
the optimum allocation.
State whether following statements are true or false. 04
1 An unordered estimator has smaller variance than ordered
estimator.
22) In sample survey, non-response error arises due to defective
frame and faulty selection of sampling units.
3 In proportional allocation of sample in stratified sampling is more
precise than optimum allocation.
4 The main impact of the non-response error is that it introduces
bias in estimator.
Q.2 Answer the following: 06
Describe cumulative total method for PPS sampling.
Describe a procedure for obtaining a sample of size n from a
population of size N using SRSWOR method.
Write short notes on the following: 08
Neyman allocation
Murthy's estimator
Q.3 In SRSWOR derive an unbiased estimator of a population mean and
its sampling variance.
07
What is proportional allocation? Derive the variance of the estimator
of the population mean under this allocation.
07
Q.4 Define Horvitz-Thompson estimator for population total. Show that it
is unbiased and obtain its variance.
07
Bring out similarities and differences between cluster sampling and
stratified sampling.
07
Q.5 What is double sampling? Explain any one practical situation where
double sampling is appropriate.
07
Explain the problem of non-response and any technique to deal with
non-response.
07
Q.6 Explain the ratio and regression methods of estimation. 07
Make a comparison between the ratio and regression estimators in
terms of MSE and state when the ratio estimator can be more
efficient than the regression estimator.
07
Q.7 Develop Des Raj's ordered estimator of population mean based
sample size 2. Show that it is unbiased.
07
Derive the sampling variance of the systematic sample mean in
terms of intra class correlation.