M.Com. (Semester II) (CBCS) Examination Oct/Nov-2017
ADVANCED STATISTICS
Day Date: Monday, 20-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: All questions are compulsory.
Figures to the right indicate full marks.
Each question carries equal marks.
Use of soundless calculators are allowed.
Q.1 Choose the alternatives given below. 14
A finite subset of statistical individuals in a population is called a
Sample Population
Census None of these
The statistical constants of the population eg. Population mean, Population
variance etc. are usually referred to as
Statistics Parameters
Constants None of these
The number of possible samples of size n that can be drawn from a finite
population of size N is
1
− 1 None of these
The aggregate of the various values of the statistic under consideration so
obtained may be grouped into a frequency distribution, which is known as the

Frequency distribution
Sampling distribution of the statistics
Probability distribution
None of these
Other things being equal, as the sample size increases, the reliability and
accuracy of the results tend to
More Less
Same None of these
Error occurred due to faulty demarcation of sampling units, is a
Sampling error Non sampling error
First kind of error None of these
The errors committed during presentation and printing of tabulated results is
a
Sampling error Non sampling error
First kind of error None of these
The main merit/s of sampling technique over the census method
Less time Reduced cost
Greater scope All these above
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SLR-CJ-22
SRS is the technique of selecting the sample in such a way that each of
samples has as equal probability of being selected.

1



1

None of these
10) The simplest method of selecting a random sample is the
Lottery system Use of random number table
Both a b None of these
11) In srswor, the sample mean square is an unbiased estimate of the
Population variance Sample variance
Population mean square None of these
12) If the population size N is very large or if sample size n is very small
compared to then finite population correction (f.p.c.) tends to

0 None of these
13) In optimum allocation of sample sizes to various strata so that
Var is minimum for fixed n
Var is minimum for fixed total cost
Total cost C is minimum for fixed value of Var
All of the above
14) The main disadvantages of systematic sampling is
Samples are not random
N is not a multiple of n
Unbiased estimate of Var is not possible
All of the above
Q.2 What are the main steps involved in a sample survey? Discuss them briefly. 07
What is a stratified random sampling? When will you use if? 07
Q.3 Explain proportional allocation and Neyman's allocation in stratified random
sampling.
07
Define systematic sampling. State if's various merits and demerits with SRS. 07
Q.4 Attempt any one of the following. 14
Define SRS. Show that sample mean in srswor is an unbiased estimate of
population mean. Find Var .
Describe the rule for determining the sample sizes to be allocated to different
strata of Neyman's allocation
Q.5 Attempt any one of the following. 14
Prove that stratified sampling mean is an unbiased estimate of the population
mean. Find V .
How does sampling without replacement differ from that with replacement?
Which of them give lower value of S. D. of sample mean? Explain by
considering samples of size two from a population consisting of the five
numbers 11.