M.Sc. Statistics (Semester II) (CBCS) Examination, 2017
SAMPLING THEORY
Day Date: Friday, 28-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: Attempt five questions.
Q. No.(1) and Q .No(2) are compulsory.
Answer any three questions from Q.3 to Q.7
Figures to the right indicate full marks.
Q.1 Select the correct alternatives. 05
Which one of the following method gives a random sample of size 3
with replacement from a population of 6 units numbered 1 to
Select even numbered units.
Select odd numbered units.
Select a unit according to the outcome of an unbiased die.
Select prime numbered units.
If an investigator selects districts from a state and farmers from
selected districts then such a sampling procedure is known as
Cluster sampling. Two stage sampling.
Double sampling. Systematic sampling.
A simple random sample of 20 units is drawn from a population of
1000 units. The probability that specified unit is selected in the 10th
draw is




Ratio estimator is unbiased if


The intra-class correlation can attain value 1 when the
efficiency of systematic sampling relative to SRSWOR is




Fill in the blanks: 05
Failure to measure some of the units in selected sample is
error
If 10 units are drawn from a population of 100 units, then sampling
fraction is
Cluster sampling helps to cost of survey.
Stratified sampling is not preferred when the population is
The Census Bureau in India take a complete population count every
Page 2 of 2
years.
State whether the following statements are True or False: 04
If the population exhibits a linear trend, then systematic sampling is
more efficient than SRSWOR design.
In PPS sampling the probability of drawing any specified unit at
given draw is same.
Sampling error is absent in a complete enumeration.
Deep stratification is a technique used to deal with non-response
errors.
Q.2 Answer the following: 06
Describe cumulative total method for drawing PPSWR samples.
Explain linear systematic sampling scheme
Write short note on the following 08
Deming's technique
Deep Stratification
Q.3 Describe a procedure for obtaining sample of size n from a population of
size N using SRSWR and SRSWOR methods.
07
In SRSWR, suggest an unbiased estimator of population mean and
derive its sampling variance.
07
Q.4 Describe Midzuno sampling design; obtain single and double inclusion
probabilities.
07
Prove that with stratified random sampling, an unbiased estimator of the
variance of is
Var
Σ
07
Where the notations have their usual meanings.
Q.5 Define Desraj's ordered estimator for the population total. Examine it for
unbiasedness and obtain its variance.
07
Derive the sampling variance of systematic sampling interms of intraclass
correlation.
07
Q.6 Define Horvitz -Thompson estimator for a population total obtain its
expected value and sampling variance.
07
Discuss the problem of non-sampling errors and method of dealing with
this problem.
07
Q.7 Define linear regression estimator for population mean. Investigate its
Properties under SRSWOR scheme.
07
Define ratio estimator and obtain approximate expression for its bias and
mean square error.