Unit wise important questions
B.Sc (M.S.Cs)-III Year Subject: Statistics, Paper: III
UNIT-I
1. Explain the
principal steps involved in a sample survey.
2. (i). Distinguish between SRSWOR and SRSWR with
examples.
(ii). In SRSWOR, show that the Probability of
selecting a specified unit at any given draw is equal to the probability
of selecting it at the first draw.
3. In SRSWOR,
show that
(i). Sample mean square is an unbiased
estimator of population mean square.
(ii).
V(
n)= {(N-n)/Nn} S2
n)= {(N-n)/Nn} S2
4. Explain the
purpose of stratification in sample survey.
Show that V(n)R 
V(st)prop in usual notations.
n)R V(st)prop in usual notations.
5.
In usual notations, prove that the systematic sample mean is more efficient
than the mean of a simple random sample taken without replacement
than the mean of a simple random sample taken without replacement
if S2wsy S2.
S2.
6.
With the usual notations, Prove that V(st)opt 
V(st)prop V(n)wor
st)opt V(st)prop V(n)wor
7. In Neyman allocation of stratified random
sampling prove that V(st) is minimum for fixed total sample size n if ni
Ni Si .
st) is minimum for fixed total sample size n if ni
Ni Si .
8. In
stratified random sampling , optimum allocation. Prove that, V(st) is
minimum
if ni Ni Si / 
i
st) is
minimum
if ni Ni Si / i
9.
If a population consists of a linear trend , then prove that
V(Yst) < V(Ysys) <V(Yn)R
10.
Explain sampling and non-sampling errors.
UNIT-II
1.
Explain the statistical analysis of one way classification.
2.
Describe the technique of the analysis of variance. Explain ANOVA two way
classification.
3.
Explain the principles of experimental design.
4.
Explain the missing plot technique in RBD.
5. Explain M*M Latin square design.
6. Explain efficiency of RBD over CRD.
7.
Explain efficiency of LSD over RBD.
8. Explain the missing plot technique in LSD.
9. Derive expectation of various sum of
squares one way classification.
10. Explain statistical analysis of CRD with
merits and demerits.
UNIT-III
1. What are the
components of time series mention its uses.
2. Explain
secular trend in time series and give the methods of semi-average and moving
averages for measuring trend.
3. What are
seasonal variations?.Explain ratio to trend method for measuring seasonal
variations.
4. Explain link
relative and ratio to moving averages methods for measuring seasonal variations.
5. How do you
fit a modified exponential curve and Gompertz curve to a time series data.
6. What is
logistic curve? Explain various methods of fitting logistic curve.
7. What are the
economic barometers? Discuss their advantages as well as the limitations.
8. Define
Index numbers. Describe steps in construction of index numbers.
9. What is cost
of living index number? Explain the steps in the construction of cost of living
index number. Mention the uses.
10. Explain
consistency tests for index numbers. Prove that fisher index number is an ideal
index number.
11. Explain the
concepts of base shifting, splicing, and deflation of index numbers.
12. Define national income. Explain the difficulties
in estimation of national income.
13. What are the functions of CSO and NSSO.
UNIT-IV
1. Explain
various rates of measuring mortality. Discuss its merits and demerits.
2. Explain the
difference between crude death rate and standardizing death rate. Give briefly
the direct and indirect method of finding standardizing death rates.
3. Define life
table. Explain in detail the construction and uses of life tables.
4. Explain
various measures of fertility. Discuss merits and demerits of these measures.
5. Explain GRR
and NRR for measuring population growth.
6.Define demand,
supply, equilibrium price. Describe demand and supply curves.
7. Describe Leontief’s method of estimating price
elasticity of demand for time series data and give its assumptions and
limitations.
8. Describe Pigou’s method of estimating price
elasticity of demand for time series data and give its limitations.
9. Define demand
function. Explain constant price elasticity of demand.
10. Describe
Pareto’s law of income distribution. Give two few situations where Pareto’s law
holds good.
Unit
wise important questions
B.Sc
(M.S.Cs)-III Year Subject:
Statistics, Paper: IV
UNIT-I
1. What is meant
by statistical quality control? Discuss briefly its need and utility in industry.
2. Give the
statistical basis for Schewartz control charts. Explain the construction of
control chart for Mean and Range.
3. Distinguish
between defect and defective. Explain the statistical basis and construction of
‘p’ and ‘np’ charts.
4. What do you
understand by control charts for variables? Give the construction of mean and S.D
chart.
5. Explain the construction
of control chart for number of defects and give applications of ‘C’ chart.
6. Explain the construction
of p chart for fixed and varying sample sizes.
7. Explain the construction
of np chart for fixed and varying sample sizes.
8. Explain the
concepts of process capability index and six-sigma.
9. Distinguish
between control limits, specification limits and tolerance limits.
UNIT-II
1. Define the
terms AQL, LTPD, consumer’s risk and producer’s risk.
2. Distinguish
between process control and product control. State the different types of
acceptance sampling plans explaining their merits and demerits.
3. Explain
single sampling plan procedure for attributes and obtain its OC and ASN
functions.
4. Explain
double sampling plan procedure for attributes with OC and ASN curves.
5. Define i).Reliability ii).Hazard rate iii).Failure density iv).Series and parallel configurations.
6. Explain
exponential distribution as life model and its lack of memory property in view
of reliability.
7. Explain the
method to compute the reliability of a system having series configuration and
parallel configuration.
8.Explain series
system, parallel system, and k out of n system with examples.
Note:
Problems on Reliability are also important.
UNIT-III
1. Explain the
scope of operations research.
2. Define the
following terms a) basic solution b) basic feasible solution
c) degenerate solution d) optimum solution
3. Define convex
set and state their properties. State and prove fundamental theorem of LPP.
4. (i). Explain
the procedure of graphical method for solving a LPP.
(ii). Define OR. Explain canonical and
standard forms of LPP.
5. When are
artificial variables used? Explain two-phase simplex method of solving a LPP.
6. Give the
simplex algorithm to solve a LPP.
7. Explain the
concept of duality and dual-primal relationship with an example.
8. Explain dual
of a symmetric LPP. Show that dual of a dual is a primal with an example.
9. What is
degeneracy in LPP? When does it occur? How is it resolved?
10. What are
surplus and artificial variables? Explain Big-M method to solve a LPP.
UNIT-IV
1. Stating
important assumption define Transportation problem. Explain VAM for obtaining
initial basic feasible solution of a transportation problem.
2. Define
balanced and unbalanced transportation problem. Explain NWCR and MMM for obtaining
initial basic feasible solution of a TP.
3. Explain MODI
method of solving TP for optimum solution.
4. Explain
transportation problem and show that it is a special case of LPP.
5. What is
degeneracy in transportation problem? How is it resolved?.
6. Define
assignment problem as a special case of LPP and TP. Explain Hungarian method to
solve an assignment problem.
7. (i). How an
unbalanced Assignment and Transportation problems are balanced? Explain with examples.
(ii). How an assignment problem for
maximization is solved? Explain.
8. Explain
stepping stone method to obtain an optimum solution for a balanced
transportation problem.
9. What is
sequencing problem? Give Johnson’s algorithm to solve two machine ‘n’ jobs
sequencing problem.
10. Explain the
job sequencing algorithm for n jobs on three machines.
11. Explain the procedure
of travelling salesman problem and transshipment problem.
Note: Unit III
and IV Problems are also important.
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