M.COM. (Semester-II) (CBCS) Examination, 2017
ADVANCED STATISTICS (Paper II)
Day Date: Friday, 21-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
N.B. All questions are compulsory.
Figures to the right indicate full marks.
Each questions carry equal marks.
Use of soundless calculators is allowed.
Q.1 Select the correct answer from multiple options given. 14
A group of all the individuals under study is called
Sample Population
Census None of these
Statistical measures computed form sample observation alone eg.
Sample mean, sample variance etc, have been termed as
Statistic Parameter
Constant None of these
The standard deviation of the sampling distribution of a statistic is
known as its
Sampling error Standard error
Non sampling error None of these
A method of collecting data from few selected units of sub-group
of population is known as
Census method Population method
Sampling method None of these
Which one of the following is are important principles of sample
survey?
Statistical regularity Validity
Optimization All these
Faulty planning or definition creates an error such type of error is
called as
Sampling errors Non sampling errors
Errors None of these
A technique of drawing a sample in such a way that each unit of
the population has an equal and independent chance of being
included in the sample is called as
Simple random sampling Stratified sampling
Systematic sampling None of these
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Generally which Random Number tables are referred to draw a
sample?
Tippet's Fisher's
Kendall's None of these
In Srswor, the variance of sample mean is given by
10) If is a sampling fraction, then finite population correction is
given by
f f 1
1 f None of these
11) Srswor provides a estimator of relative to srswor.
More efficient Less efficient
Equal efficient None of these
12) If population under study is not homogeneous and formed by
different groups strata, them which method of sampling is proper?
SRS Stratied sampling
Systematic sampling None of these
13) If in stratified sampling then allocation to each
stratum is called as
Proportional allocation Nayman's allocation
Optimum allocation None of these
14) The selection of every Kth strip in forest survey for estimation of
timber, which method of the following is more convenient?
SRS Stratified sampling
Systematic sampling None of these
Q.2 Define: 07
1. SRS without replacement
2. SRS with replacement
What do you meant by stratified Random sampling? Give
essential characteristics of stratified Random Sampling.
07
Q.3 What is a systematic Sampling? Give illustration where such
sampling is usual.
07
Define SRS and prove that sample mean is an unbiased
estimate of the population mean.
07
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Q.4 Attempt any one of the following. 14
In SRS find the variance of sample mean.

Q.5 Attempt any one of the following. 14
Compare proportional allocation, Neyman's allocation and
optimum allocation in stratified Random Sampling.
Consider a population of 6 units with values Write
down all possible samples of 2(without replacement) from this
population and verify that sample mean is an unbiased estimate
of the population mean. Also calculate its sampling variance and
verify that if agree with the formula for the variance of the
sample mean.