M.Sc. (Semester II) (CBCS) Examination Nov/Dec-2018
Statistics
SAMPLING THEORY
Time: 2½ Hours Max. Marks: 70
Instructions: Attempt five questions.
Q. No. and Q. No. are compulsory.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Q.1 Choose the correct alternative: 05
If we have a sample of size n from a population of N units, the finite
population correction is












Under proportional allocation, the size of sample from each stratum
depends on
Total sample size Size of the stratum
Population size All the above
The problem of non-response
has no solution can be solved
is meaningless None of these
The total number of samples of size 2 that can be drawn with
replacement from a population of 10 units is
90 100
45 50
In SRSWOR, sample of size 5 units is drawn from a population of size 20
units. The probability that a specified unit is selected in 3rd draw is


1
4

1
5

1
3

1
2
Fill in the blanks: 05
Probability of any one sample of size n being drawn out of n units is
When the population size N is multiple of sample size n then
systematic sampling is appropriate.
A random start automatically fixes the subsequent selections of sample
units in sampling method.
Deming's technique deals with
Cluster sampling is efficient if clusters are more homogenous.
State whether following statements are true or false: 04
Horvitz-Thompson estimator is commonly used in PPSWR sampling
schemes.
Hanson-Hurvitz technique is used for dealing with the problem of nonresponse.
Deep stratification technique is used to deal with non-sampling errors.
IN PPS sampling some units may be selected with probability one.
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SLR-VR-481
Q.2 Answer the following. 06
Describe circular method of drawing systematic samples.
Define ordered and unordered estimators.
Write short notes on the following: 08
Non-sampling errors
Murthy's unordered estimator
Q.3 Describe the procedure for drawing a simple random sample of size n
without replacement from a finite population of size N. Obtain the
probabilities of drawing a specified sample in simple random sampling with
and without replacement.
07
Let … . be measurements with respect to characteristic Y on the
units of simple random sample drawn without replacement from a population
of size N.
Show that,


where
1



N
i
yi Y
1
2
07
Q.4 Explain the principles of forming strata and clusters. What are similarities
and differences between stratified sampling and cluster sampling?
07
Describe linear systematic sampling. Derive the sampling variance of
unbiased estimator of population mean under this scheme.
07
Q.5 Outline regression method of estimating a population mean. Assuming
SRSWOR, derive the MSE of estimator.
07
What are almost unbiased ratio type estimators? Provide two examples. 07
Q.6 Define Midzuno scheme of sampling. Obtain single and double inclusion
probabilities.
07
Develop Des Raj's ordered estimator of population mean based sample
size2. Show that it is unbiased.
07
Q.7 Discuss Hansen-Hurwitz techniques of tackling the problem of non-response
giving all the details.
07
In SRSWOR of n clusters each containing M elements from a population of
N clusters. Show that the sample mean is an unbiased estimator of
population mean and find its variance.