Master of Science I (Statistics)Examination: Oct/Nov 2016
Semester II (New CBCS)
SLR No. Day
Date Time Subject Name Paper
No. Seat No.
SLR SB
689
Saturday
26/11/2016
10.30 AM
to
01.00 PM
Sampling Theory
C
X
Instructions: Answer any five questions.
Q. No. and Q. No. are compulsory.
Attempt any three from Q. No. to Q. No.
Figures to the right indicate full marks.
Total Marks:70
Q.1 A. Select the correct alternative: 05
Systematic sampling means
Selection of any n units
Selection of n largest units
Selecting n units situated at equal intervals.
Selecting n continuous units
In simple random sampling, the ratio estimator is
Always unbiased Always biased
Minimum variance unbiased None of the above
A border check post stops every passenger van. Which one of the
following procedure is adopted?
Random sampling Purpose sampling
Systematic sampling Complete enumeration
Simple regression estimate of population mean is given by
Probability of any one sample of size n being drawn out of n units is
B. Fill in the blanks: 05
Under Midzuno sampling scheme, the units from second draw are
selected with probabilities.
Errors introduced in editing, coding and tabulating the results is
Under SRSWR, the sample unit can occur in the sample.
Strata in stratified sampling should be internally
Under proportional allocation, the sample size for ith stratum is
proportional to
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C. State whether following statements are true or false: 04
Horvitz-Thompson estimator is commonly used in PPSWR sampling
schemes.
Ratio estimators are generally biased.
Deciding the sample size for each stratum is known as allocation problem.
SRSWR scheme is always more precise than SRSWOR Scheme for a
given sample.
Q.2 A. In SRSWOR scheme, show that the sample mean is an unbiased estimator for
the population mean.
03
B. Explain systematic sampling with example. 03
C. Write short note on the following: 08
Desraj ordered estimator
Method of collapsed strata
Q.3 A. Explain the sampling method and census method. Give advantages of
sampling method over census method.
07
B. Explain cluster sampling and two stage sampling. 07
Q.4 A. What is proportional allocation? Drive the variance of estimator of the
population mean under this allocation.
07
B. In SRSWOR, derive an unbiased estimator of population mean and its
sampling variance.
07
Q.5 A. Define PPSWR sampling. Describe Lahiri's method and cumulative total
method for drawing PPSWR samples.
07
B. Describe Midzuno sampling design. Obtain the expression for first and second
order inclusion probabilities.
07
Q.6 A. Describe unbiased and almost unbiased ratio type estimators. 07
B. Define linear regression estimator for population mean. Is it unbiased?
Assuming SRSWOR, derive MSE of the estimator.
07
Q.7 A. Explain in detail Deming's technique in the presence of non response in
surveys.
07
B. Define Horvitz-Thompson estimator for population mean. Examine it for
unbiasedness and derive its variance.
07
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