Semester - V Syllabus

                Osmania University

B.Sc. III Year V Semester (CBCS): Statistics Syllabus

Paper-V: Sampling Theory, Time series, Index Numbers and Demand Analysis

(DSC-2E)

              (3 Hours Per Week with 3 Credits and 100 Marks)

UNIT-I

Sample Surveys: Concepts of Population, Sample, Sampling unit, Parameter, Statistic, Sample frame and Standard error. Principal steps in sample surveys - need for sampling, census versus sample surveys, sampling and non- sampling errors, sources and treatment of non-sampling errors, advantages and limitations of sampling.

Sampling Methods: Types of sampling: Subjective, probability and mixed sampling methods. Methods of drawing random samples using with and without replacement. Estimates of population mean, total, and proportion, their variances and the estimates of variances in Simple Random Sampling With and Without Replacement.

UNIT-II

Estimates of population mean, total, and proportion, their variances and the estimates of variances in the following methods.

(i) Stratified Random Sampling with Proportional and Neyman allocation, and

(ii) Systematic Sampling when N = nk.

Comparison of their relative efficiencies. Advantages and disadvantages of SRS, Stratified and Systematic sampling methods.

Time series: Time series and its components with illustrations, additive, multiplicative and mixed models. Determination of trend by least squares and moving average methods. Growth curves and their fitting with reference to Modified exponential, Gompertz and Logistic curves. Determination of seasonal indices by Ratio to moving average, ratio to trend and link relative methods.

UNIT-III

Demand Analysis: Introduction. Demand and supply, price elasticity of supply and demand. Methods of determining demand and supply curves, Leontief’s ,Pigous’s methods of determining demand curve from time series data, limitations of these methods Pigou’s method from time series data. Pareto law of income distribution curves of concentration.

Index Numbers: Concept, construction, uses and limitations of simple and weighted index numbers. Laspeyer’s, Paasche’s and Fisher’s index numbers, criterion of a good index numbers, problems involved in the construction of index numbers. Fisher’s index as an ideal index number. Fixed and chain base index numbers. Cost of living index numbers and wholesale price index numbers. Base shifting, splicing and deflation of index numbers.

Reference Books:

1. V.K. Kapoor and S.C. Gupta : Fundamentals of Applied Statistics. Sultan Chand

2. Parimal Mukhopadhyay : Applied Statistics, New Central Book agency.

3. Daroga Singh and Chowdhary: Theory and Analysis of Sample survey designs. Wiley Eastern.

4. M.R.Saluja : Indian Official Statistics. ISI publications.

5. B.L.Agarwal: Basic Statistics.New Age publications.

6. S.P.Gupta : Statistical Methods. Sultan Chand and Sons.

7. Anuvartita Sankhyaka Sastram – Telugu Academy.

8. Arora, SumeetArora,S.Arora: Comprehensive Statistical Methods. S.Chand.

9. A.M.Goon, M.K.Gupta, B. Dasgupta: Fundamentals of Statistics Vol II World Press Private Ltd.,Calcutta

10. A.M.Goon,M.K.Gupta,B.Dasgupta An outline of Statistical Theory Vol II World Press Private

Ltd.,Calcutta17.

Practical Paper-V: Theory Paper V and Elective VI A

(with 2 HPW, Credits 1 and 25 Marks)

Section – A

Estimation of Population mean, population total and variance of these estimates by

1. Simple random sampling with and without replacement. Comparison between SRSWR and

SRSWOR

2. Stratified random sampling with proportional and optimum allocations. Comparison between

proportional and optimum allocations with SRSWOR

3. Systematic sampling with N = nk. Comparison of Systematic sampling with Stratified and

SRSWOR

4. Measurement of trend by method of least squares and moving averages.

5. Determination of seasonal indices by the method of Ratio to moving averages.

6. Determination of seasonal indices by the method of Ratio to trend.

7. Determination of seasonal indices by the method of link Relatives.

Section - B

8. Construction of X , R and s - charts.

9. Construction of p, np, charts with fixed and varying n.

10. Construction of c and u charts.

11. Designing a single sampling plan and construction of its OC and ASN curves.

12. Designing a double sampling plan and construction of its OC and ASN curves.

Note: The question paper consists of TWO sections. Section A Consists of 2 Questions from

Section A of Practical paper V and Section B consists of 2 questions from Section B of

Practical paper V.

Osmania University

B.Sc. III Year V Semester (CBCS): Statistics Syllabus

Paper-VI A: Statistical Quality Control and Reliability (DSC-2E)

(3 Hours Per Week with 3 Credits and 100 Marks)

Unit –I

Statistical Quality Control: Importance of SQC in industry. Dimensions of quality, Statistical basis of Shewart control charts. Construction of control charts for variables (mean, range and standard deviation) and attributes (p , np with fixed and varying sample sizes) and their Interpretation.

Unit –II

Control charts for attributes (c and u charts with fixed and varying sample sizes) and their Interpretation.

Construction of control charts for Natural tolerance limits and specification limits, process capability index and modified control charts.

Unit –III

Acceptance sampling plans:. Concept of AQL and LTPD. Producers risk and consumer’s risk, Single and Double sampling plans for attributes and their OC and ASN functions. Design of single and double sampling plans for attributes using Binomial and Poisson distributions. Construction of OC and ASN functions.

Reliability: Introduction. Hazard function, Exponential distribution as life model, its memory- less property. Reliability function and its estimation.

System reliability - series, parallel and k out of N systems and their reliabilities with simple examples.

Reference Books:

1. D.C. Montgomary: Introduction to Statistical Quality Control. Wiley

2. V.K. Kapoor and S.C.Gupta L Fundamentals of Applied Statistics. Sultan Chand

3. Parimal Mukhopadhyay : Applied Statistics . New Central Book agency

4. Anuvartita Sankhyakasastram – Telugu Academy.

5. R.C.Gupta: Statistical Quality Control.

6. S.K.Sinha: Reliability and life testing. Wiley Eastern

7. L.S.Srinath: Reliability Engineering. Affiliated East-West Press.

Practical Paper-VI: MS - EXCEL

(with 2 HPW, Credits 1 and 25 Marks)

Time Series Analysis

1. Measurement of trend by method of least squares and moving averages.

2. Determination of seasonal indices by the method of Ratio to moving averages.

3. Determination of seasonal indices by the method of Ratio to trend.

4. Determination of seasonal indices by the method of link Relatives.

Index Numbers

5. Base shifting, splicing and Deflation.

Statistical Quality Control

6 Construction of x , R and s charts.

7 Construction of p and np charts with fixed n.

8 Construction of p and np charts with varying n.

9 Construction of c and u charts.

Demand Analysis

10 Construction of Lorenz curve.

11 Fitting of Pareto law to an income data.

Note 1 : Training shall be on establishing formulae in Excel cells and deriving the results. The excel output shall be exported to MSWord for writing inferences.

Note 2 : The question paper consists of TWO sections. Section A Consists of 2 Questions from Paper VI Practical and Section B consists of 2 questions on MS – Excel from Semesters I and III respectively.