M.Com. (Semester II) (CBCS) Examination Nov/Dec-2018
ADVANCED STATISTICS (Paper II)
Time: 2½ Hours Max. Marks: 70
Instructions: All questions are compulsory.
Figures to the right indicate full marks.
Each question carries equal marks.
Use of soundless calculators is allowed.
Q.1 Choose the alternatives given below. 14
A Sample is population.
Complete Subset of
Set of all units None of these
Sampling is mainly classified as sampling.
Probability and Non-probability Simple random and Stratified
Simple random and systematic All of the above
A selected unit is replaced back into population, then it is
Simple random sampling without replacement
Simple random sampling with replacement
Systematic sampling
None of these
From the set of 10 elements 4 units are selected by SRSWOR then sampling
fraction is
0.6 0.4
4 10
Sample mean is unbiased estimator of population mean in sampling.
Simple random Stratified
Both and Neither nor
If Vwr represents variance of sample in simple random sampling with
replacement and Vwor is variance of sample mean in without replacement,
then
Vwr Vwor Vwor Vwr
Vwr Vwor None of these
In SRSWOR finite population correction is given by
All of above
In linear systematic sampling where there are possible
systematic samples.
n k
n/k N/k
If there is an error due to unit non-response then it is
Sampling error Non-sampling error
Error None of these
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10) In the population of 5 sampling units a random sample of size 2 is to be
selected with replacement then, there are total number of
possible samples.
5 25
10 3
11) In stratified sampling same numbers of units are drawn from each stratum,
then it is
proportional allocation equal allocation
optimal allocation none of these
12) In a study of attitudes to university policy, a researcher interviewed 150 first
year, 130 second year and 100 third year students, the sampling procedure
used is
probability sampling stratified sampling
systematic sampling quota sampling
13) All the students in a college are surveyed, then it is
quota sampling simple random sampling
census none of these
14) Stratified sampling is useful when population is
Homogeneous Heterogeneous
Mixed None of these
Q.2 Illustrate with an example. 07
Stratified random sampling
Systematic sampling
For SRSWR, show that sample mean is unbiased estimator for population
mean. Also find variance of the estimator.
07
Q.3 What is simple random sampling with and without replacement? Illustrate with
example.
07
Explain different allocation procedures in stratified random sampling. 07
Q.4 Attempt any one of the following. 14
Obtain an unbiased estimator of population mean in stratified random
sampling and hence find its variance.
From the population draw a SRSWOR of size 3. Obtain sample
mean and also find its standard error.
Q.5 Attempt any one of the following. 14
Show that Neyman's allocation is more efficient than proportional and equal
allocation in stratified sampling.
What is non-sampling errors? Explain at least two non-sampling errors.