CLASS: B.STAT.
13N/260
St. JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002
SEMESTER EXAMINATIONS – NOVEMBER 2013
TIME: 3 Hrs.
MAXIMUM MARKS: 100
SEM
SET
PAPER CODE
TITLE OF THE PAPER
V
2011
11UST530210
SAMPLING THEORY
SECTION – A
Answer all the questions:
20 x 1 = 20
Choose the correct answer:
1. A sample consists of:
a) All units of the population
b) 50% units of the population
c) 5% units of the population
d) Any fraction of the population
2. Probability of drawing one unit at each selection remains same in:
a) SRSWOR
b) SRSWR
c) Both a) and b)
d) None of a) and b)
3. Stratified sampling comes under the category of:
a) Unrestricted sampling
b) Subjective sampling
c) Purposive sampling
d) Restricted sampling
4. Systematic sampling means:
a) Selection of n contiguous units
b) Selection of n units situated at equal distance
c) Selection of n largest units
d) Selection of n middle units in a sequence
5. Probability of including a specified unit in a sample of size n selected out of N units is
a)
b)
1
1
c)
n
n
N
d)
N
N
n
Fill in the blanks:
6.
Sampling is ________ of the population.
7.
A population consisting of an unlimited number of units is called as an ________ population.
8.
Stratified sampling is appropriate when population is ________.
9.
Systematic sample ________ be said to give more reliable results then a random sample.
10. A value of the estimator is an ________ of the parameter.
State True or False:
11. In a hypothetical population all sampling units are imaginary.
12.
 N
 
 N
n
The probability of selection of any one sample out of 
  sample is
n
13.
Under SRSWR, the same item can occur more than once in the sample.
14.
Population is divided into substrata (or) cell under two way stratification.
15.
Double sampling is useful in ratio and regression estimation method.
Match the following:
16.
Nn
N 1
- a) Heterogeneous
N
17.
n
N
18.
19.
20.
Optimum allocation
Stratified Random sampling
Non sampling error
- b) Neyman
- c) Inadequacy
- d) Finite population correction
- e) Sampling fraction
SECTION – B
Answer all the questions:
5 x 4 = 20
21. a. Explain the limitations of sampling.
OR
22.
b.
Discuss non-sampling errors.
a.
Explain the selection procedure of a simple random sample.
OR
b.
In SRSWOR, prove that the sample mean is an unbiased estimate of the population mean
i.e.,
23.
a.
E( yn )  YN .
Explain the principal advantages of stratified random sampling.
OR
24.
b.
Describe the proportional allocation and optimum allocation, in stratified random
sampling.
a.
Explain about systematic sampling.
OR
b.
Explain the advantages of systematic sampling over simple random sampling.
25.
a.
Explain “Ratio estimators” and regression estimator.
OR
b.
R̂ is given by
In SRSWOR prove that for large n, an approximation of the variance of
N y  R 2


1

f
i
xi
Var (R̂ ) ~


nx 2 i 1 N  1
SECTION – C
Answer any FOUR questions:
26. Explain in detail the principal steps in a sample survey.
27.
28.
29.
In
prove
that
the
variance
of
the
sample
mean
is
given
S2 N  n
Var yn   
n
N
Prove that the Var yst  is minimum for fixed total size of ith sample(n) if ni NiSi
Obtain the variance of the estimate of mean in systematic sampling.
i.e.,
30.
SRSWOR,
4 x 15 = 60
Var ( ysys ) 
N  1 2 n  1k 2
S 
 Swsy
N
N
Show that to the first order of approximation, the
Var (R̂ ) 
y
1  f  S2  R 2S2  2RS
nx
2
x
**************
  can be expressed as
Var R̂
xSy

by