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7Govt. College for Men (Autonomous): KadapaDepartment of Statistics

Basic curricular Format under Modular and CBCS System(w.e.f. 2016 – 2017)

Semester: I Name of the Module: Descriptive Statistics and Probability

No. of Hours/week : 04 credits 3

UNIT -IIntroduction to Statistics, Definition, Origin and development of Statistics, Applications and limitations of statistics. Types of Data: Concepts of population and sample, quantitative and qualitative data, cross-sectional and time-series data, discrete and continuous data, different types of scales. Collection of Data: Primary data and Secondary data – its major sources. Presentations of data: Construction of frequency table (one and two factors) Diagrammatic(Bar and Pie) and Graphical representations(Histogram, frequency curves, Ogives) of ungrouped and grouped data.

Unit - IIConcept of Central Tendency- Various measures of central tendency and their merits and demerits, properties and applications of central tendency. Use of other partition values. Concept of Dispersion-Various measures of dispersion and their merits and demerits, properties and applications of dispersion.

Unit - IIIMoments: Raw moments for grouped and ungrouped data. Moment about an arbitrary constant for grouped and ungrouped data Central moments for grouped and ungrouped data. Effect of change of origin and scale. Sheppard’s corrections. Relations between central moments and raw moments (up to 4thorder ). Symmetric frequency distribution. Skewness and Kurtosis: Concept of Skewness of frequency distribution- positive skewness and negative skewness. Measures of skewness- Karl pearson’s cofficient of skewness - Bowley’s coefficient of Skewness,- Based on mooments( β1, γ1 ). Concept of Kurtosis- lepto kurtic, meso kurtic and platy kurtic frequency distributions. Measures of Kurtosis based on moments ( β2, γ2 ).

UNIT -IVProbability: Basic concepts in probability-deterministic and random experiments, trail, outcome, sample space, event, and operations of events, mutually exclusive and exhaustive events, and equally likely and favourable outcomes with examples. Mathematical, Statistical and

axiomatic definitions of probability with merits and demerits. Properties of probability based on axiomatic definition. Conditional probability and independence of events. Addition and multiplication theorems for n events. Boole’s inequality and Bayes’ theorem. Problems on probability using counting methods and theorems.

Unit - VRandom Variables: Definition of random variable, discrete and continuous random variables, functions of random variables, probability mass function and probability density functions with illustrations. Distribution function and its properties. Notion of bivariate random variable, bivariate distribution and statement of its properties. Joint, marginal and conditional distributions. Independence of random variables. Measures of location, Dispersion, Skewness, Kurtosis of random variable.

Text Books:1. S.C.Gupta and V.K.Kapoor, Fundamental of Mathematical Statistics, Sultan Chand &

Sons Pvt. Ltd. New Delhi.2. S.P.Kapoor, Statistical Methods, Sultan Chand & Sons Pvt. Ltd. New Delhi.3. K.V.S. Sarma, Statistics made simple: Do it your self on PC, PHI.

Books for Reference:

1. Hogg, R.V. and Craig, A.T. (1998): Introduction to Mathematical Statistics, 4th ed. Academic Press.

2. Hoel, P.G. (1971): Introduction to Mathematical Statistics, Asia Publishing House.

3. Goon, AM., Gupta M.K and .Dasgupta B (1991): Fundamentals of Statistics, Vol.1, World Press, Calcutta.

4. Bhat B.R, Srivenkataramana T, and Madhava K.S,(1996) Statistics: A Beginner's text Vol. I, New Age International (P) Ltd.

5. G.U.Yule and M.G. Kendall (1956): An introduction to the theory of Statistics, Charles Griffin.

6. M.R. Spiegel (1961): Theory and problems of statistics, Schaum's outline series.

7. Snedecor .G.W. and Cochran W.G. (1967): Statistical methods, Iowa State University Press.

8. Anderson, T.W. and Sclove SL. (1978): An introduction to statistical analysis of data, Houghton Miffin/co.

9. Croxton FE, and Cowden D.J. (1973) Applied General Statistics, Printice Hall of India.

Question paper pattern:

Time: 3 hours Max. Marks: 60

The question paper is divided into two sections.

Section A: Consisting of 8 questions. Answer any five questions. Each question carries 4 marks. Total marks for section A is 5x4 = 20.

Section B: Consisting of 5 questions with internal choice from each unit. Each question carries 8 marks. Total marks for section B is 8x5 = 60.

Govt. College for Men (Autonomous): Kadapa (w.e.f. 2017 – 2018)

Subject: Statistics Semester: I Paper – I : Descriptive Statistics and Probability

MODEL QUESTION PAPER

Section – A

Answer any FIVE questions. Each question carry FOUR marks 5X4 = 20

1. Distinguish between Primary and Secondary data.2. Draw the Ogives and hence estimate the median.

Class: 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79Frequency: 08 32 142 216 240 206 143 13

3. Explain various measures of Dispersions.4. Explain the concept skewness and give the measure of kurtosis.5. Show that for any distribution β2 ≥ 1.6. Define Mathematical and Axiomatic approach to probability.7. If A and B are independent events then show that

(a) A and B are also independent events.(b) A and B are also independent events.

8. Define Joint, marginal and conditional distributions.

Section – B 5 x 8 =40

Answer all questions and each question carry 8 marks

Unit -I

9. Define the term “Statistics” and discuss functions and limitations. (OR)

10. Explain Primary data. Give various methods of collecting Primary data. Also mention merits and demerits.

11. What is a measure of central tendency? Explain various measures of central tendency. Give their uses.

(OR)12. Compute mean and standard deviation for the following frequency distribution.

Class: 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79Frequency: 08 32 142 216 240 206 143 13

13. Define raw and central moments and obtain relations between central moments in terms of raw moments.

(OR)14. Explain the concept skewness. Give various measures of skewness.15. State and prove addition theorem of probability for ‘n’ events.

(OR)16. (a) State and prove Baye’s theorem.

( b ) Three Urns containing white, red and black balls as follows Urn I : 2 White, 4 Red and 3 Black balls Urn II : 3 White, 2 Red and 1 Black ballsUrn III : 4 White, 5 Red and 2 Black ballsOne urn is chosen at random and drawn two balls at random from selected urn. What is the probability that the drawn two balls are white? If the balls are white what is the probability that they come from urn II.

17. Define distribution function and also explain its properties.

(OR)

18. Let X be a continuous random variable with the following probability density functionf ( x )=Kx (2−x );0≤ x≤2

= 0 otherwise

Find the constant K. Also compute mean and variance of the random variable X.

Practical - IName of the Module: Descriptive Statistics and ProbabilityNo. of Hours/week : 02 credits 2

1. Basics of Excel- data entry, editing and saving, establishing and copying a formulae, built in functions in excel, copy and paste and exporting to MS word document.(Not for The Examination).

2. Graphical presentation of data (Histogram, frequency polygon, Ogives).3. Graphical presentation of data (Histogram, frequency polygon, Ogives) using MS Excel4. Diagrammatic presentation of data (Bar and Pie).5. Diagrammatic presentation of data (Bar and Pie) using MS Excel6. Computation of measures of central tendency(Mean, Median and Mode)7. Computation of measures of dispersion(Q.D, M.D and S.D)8. Computation of non-central, central moments, 1 and 2 for ungrouped data.9. Computation of non-central, central moments, 1 and 2 for grouped data.10. Computation of central moments – Sheppard’s corrections for grouped data.11. Computation of Karl Pearson’s coefficients of Skewness and Bowley’s coefficients of

Skewness.12. Computation of measures of central tendency, dispersion and coefficients of Skew -ness,

Kurtosis using MS Excel.

Note: Training shall be on establishing formulae in Excel cells and derive the results. The excel output shall be exported to MS word for writing inference.

Govt. College for Men (Autonomous): KadapaDepartment of Statistics


Semester: IIName of the Module : Mathematical Expectation and Probability

Distributions

No. of Hours/week : 04 credits 3

UNIT-I

Mathematical Expectation: Mathematical expectation of a function of a random variable. Raw and central moments and covariance using mathematical expectation with examples. Addition and multiplication theorems of expectation. Definition of moment generating function (m.g.f), cumulant generating function (c.g.f), probability generating function (p.g.f) and characteristic function (c.f) and statements of their properties with applications. Chebyshev’s, and Cauchy-Schwartz’s inequalities and their applications.

UNIT – II

Discrete distributions: Uniform, Bernoulli, Binomial, Poisson distributions - Properties of these distributions such as m.g.f, c.g.f., p.g.f., c.f., and moments upto fourth order and their real life applications. Reproductive property wherever exists. Poisson approximation to Binomial and Negative binomial distributions.

Unit - III

Discrete distributions: Negative binomial, Geometric distributions -Properties of these distributions such as m.g.f, c.g.f., p.g.f., c.f., and moments upto fourth order and their real life applications. Reproductive property wherever exists. Hyper-geometric distribution(mean and variance only). Binomial approximation to Hyper-geometric distribution.

UNIT – IV

Continuous distributions: Rectangular, Exponential, Gamma distributions- Properties of these distributions such as m.g.f., c.g.f., c.f., and moments up to fourth order, their real life applications and reproductive property wherever exists. Beta of two kinds (mean and variance only).

Unit - V

Continuous distributions: Normal distribution- Importance of Normal distribution - Properties of normal distribution such as m.g.f., c.g.f., c.f., and moments up to fourth order, reproductive property and real life applications Normal distribution as a limiting case of Binomial and Poisson distributions. Cauchy distribution-Definition, c.f. and reproductive property.

Text Books:1. S.C.Gupta and V.K.Kapoor, Fundamental of Mathematical Statistics, Sultan Chand &

Sons Pvt. Ltd. New Delhi.2. S.P.Kapoor, Statistical Methods, Sultan Chand & Sons Pvt. Ltd. New Delhi.3. K.V.S. Sarma, Statistics made simple: Do it your self on PC, PHI.

Books for Reference: 1. Hogg, R.V. and Craig, A.T. (1998): Introduction to Mathematical Statistics, 4th ed.

Academic Press.

2. Hoel, P.G. (1971): Introduction to Mathematical Statistics, Asia Publishing House.

3. Goon, AM., Gupta M.K and .Dasgupta B (1991): Fundamentals of Statistics, Vol.1, World Press, Calcutta.

4. Bhat B.R, Srivenkataramana T, and Madhava K.S,(1996) Statistics: A Beginner's text Vol. I, New Age International (P) Ltd.

5. G.U.Yule and M.G. Kendall (1956): An introduction to the theory of Statistics, Charles Griffin.

6. M.R. Spiegel (1961): Theory and problems of statistics, Schaum's outline series.

7. Snedecor .G.W. and Cochran W.G. (1967): Statistical methods, Iowa State University Press.

8. Anderson, T.W. and Sclove SL. (1978): An introduction to statistical analysis of data, Houghton Miffin/co.

9. Croxton FE, and Cowden D.J. (1973) Applied General Statistics, Printice Hall of India.




Section A: Consisting of 8 questions. Answer any five questions. Each question carries 4 marks. Total marks for section A is 5x4 = 20.Section B: Consisting of 5 questions with internal choice from each unit. Each question carries 8 marks. Total marks for section B is 8x5 = 40.


Subject: Statistics Semester: II Paper – II : Mathematical Expectation and Probability Distributions

Section - AAnswer any FIVE questions. Each question carry FOUR marks 5X4 = 20

1. State and prove addition theorem on Expectations.2. Define characteristic function and also write its properties3. Define Binomial distribution and also find mean and Variance.4. State and prove additive property of independent Poisson variates.5. Define geometric distribution. Obtain moment generating function of geometric

distribution and also find mean and variance.6. Obtain moment generating function of gamma distribution also find mean and variance.7. Define Uniform distribution and also find mean and variance.8. Define normal distribution and explain its importance.

Section - BAnswer all questions and each question carry 8 marks 5 x 8 = 40

Unit – I

9. State and prove Cauchy-Schwartz inequality.(OR)

10. Let X be a random variable with the following probability distributionX : -3 6 9P(X=x) : 1/6 1/2 1/3

Find E(X) and E(X2) and using the laws of expectation evaluate E(2X + 1)2

UNIT - II11. Obtain the recurrence relation for the moments in Binomial distribution

(OR)12. Obtain mode of the Poisson distribution.

Unit - III13. Show that poisson distribution as a limiting case of negative binomial distribution.

(OR)14. Define Hyper geometric distribution and find mean and variance.

Unit- IV15. Explain lack of memory property of Exponential distribution.

(OR)16. Explain the Beta distribution of first and second kind.

Unit - V17. Obtain moment generating function of normal distribution.

(OR)18. Obtain the characteristic function of Cauchy distribution.

Practical - IIName of the Module : Mathematical Expectation and

Probability DistributionsNo. of Hours/week : 04 credits 2

1. Fitting of Binomial distribution – Direct method.2. Fitting of Binomial distribution – Direct method using MS Excel.3. Fitting of binomial distribution – Recurrence relation Method.4. Fitting of Poisson distribution – Direct method.5. Fitting of Poisson distribution – Direct method using MS Excel.6. Fitting of Poisson distribution - Recurrence relation Method.7. Fitting of Negative Binomial distribution.8. Fitting of Geometric distribution.9. Fitting of Normal distribution – Areas method.10. Fitting of Normal distribution – Ordinates method.11. Fitting of Exponential distribution.12. Fitting of Exponential distribution using MS Excel13. Fitting of a Cauchy distribution.14. Fitting of a Cauchy distribution using MS Excel15. .

Note: Training shall be on establishing formulae in Excel cells and derive the results. The excel output shall be exported to MS word for writing inference.

Govt. College for Men (Autonomous): Kadapa

Department of StatisticsBasic curricular Format under Modular and CBCS System

(w.e.f. 2017 – 2018)Semester: III paper: III

Name of the Module: Statistical Methods and Sampling Distributions No. of Hours/week : 04 credits 3

UNIT – I

Curve fitting: Bi- variate data, Principle of least squares, fitting of k t hdegree polynomial. Fitting of straight line ( y=a+bx), Fitting of Second degree polynomial or parabola (y=a+bx+c x2), Fitting of power curve ( y=a xb) and exponential curves of type i) y=aebxand ii) y=abx with problems.

UNIT – II

Correlation : Meaning, Types of Correlation, Measures of Correlation : Scatter diagram, Karl Pearson’s Coefficient of Correlation, Rank Correlation Coefficient (with and without ties), Bi-variate frequency distribution, correlation coefficient for bi-variate data and simple problems. Correlation ratio, concept of multiple and partial correlation coefficients (three variables only ) and properties

UNIT – III

Regression : Concept of Regression, Linear Regression: Regression lines, Regression coefficients and it’s properties, Regressions lines for bi-variate data and simple problems. Correlation vs regression. concept of multiple linear regression and partial regression.

UNIT – IV

Attributes : Notations, Class, Order of class frequencies, Ultimate class frequencies, Consistency ofdata, Conditions for consistency of data for 2 and 3 attributes only , Independence of attributes , Association of attributes and its measures, Relationship between association and colligation of attributes, Contingency table: Square contingency(ℵ 2), Mean square contingency(φ2 ), Coefficient of mean square contingency (C), Tschuprow’s coefficient of contingency (τ 2¿ .

UNIT – V

Sampling distributions: Population, Sample, Parameter, statistic, Sampling distribution, Standard error. Definition and properties of Student’s t- distribution, F – Distribution, ℵ 2 -

Distributions and its Applications, the relationship between t and F – distribution and the relationship between F and ℵ 2distribution.

List of Reference Books:

1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand&Sons, New Delhi

2. Goon AM, Gupta MK,Das Gupta B : Outlines of Statistics , Vol-II, the World Press Pvt.Ltd., Kolakota.

3. Hoel P.G: Introduction to matehematical statistics, Asia Publiushing house.4. Sanjay Arora and Bansi Lal:.New Mathematical Statistics Satya Prakashan , New Delhi5. Hogg and Craig :Introduction to Mathematical statistics. Printis Hall6. Parimal Mukhopadhyay: Mathematical Statistics. New Central Book agency.7. K.Rohatgi and A.K.Md.Ehsanes Saleh: An introduction to probability and statistics.

Wiley series.8. Mood AM,Graybill FA,Boe’s DC. Introduction to theory of statistics. TMH9. Paramiteya mariyu aparameteya parikshalu. Telugu Academy.10. K.V.S. Sarma: Statistics Made simple do it yourself on PC, PHI(latest edition)11. Gerald Keller: Applied Statistics with Microsoft excel. Duxbury. Thomson Learning12. Levin, Stephan, Krehbiel, Berenson: Statistics for Managers using Microsoft Excel.4th

edition. Pearson Publication.13. Hogg, Tanis, Rao. Probability and Statistical Inference. 7th edition. Pearson Publication.







Subject: Statistics Semester: III Paper – III : Statistical Methods and Sampling Distributions

MODEL QUESTION PAPERSection – A

Answer any FIVE questions. Each question carry FIVE marks 5X5 = 25

1. Describe the method of fitting a power curve of the type y=axb.2. Define correlation between two variables. Discuss the types of correlation. 3. Show that correlation coefficient lies between – 1 and +1.4. Write the properties of regression coefficients with at least two proofs.5. The data is given below is marks in two subjects mathematics and statistics of B.Sc

students.mathematics statistics

Average marks

39.5 49.5

Standard deviation

10.8 16.8

The correlation coefficient between marks in two subjects is 0.42

(a) Estimate the marks in statistics if the marks in mathematics is 52.(b) Find angle between two regression lines.

6. Define consistency of the data. Discuss the conditions for consistency of the data for three attributes.

7. Define the terms (i) Population (ii) Sample (iii) Parameter (iv) Statistic (v) Sampling distribution

8. Define t- distribution and write down its applications.Section – B

Answer any FIVE questions, each question carries 10 marks 5X10=50 Marks

9. Explain the method of least squares of fitting a second degree polynomial to the given data?

OR10. Fit a straight line of the given data

X : 149 157 142 140 138 142 145 142 144 140 146 144

Y : 129 110 126 130 141 129 127 127 119 118 119 131

11. The following table gives the soil temperature and germination time at various places calculate the coefficient of correlation?

OR12. Obtain Spearman’s rank correlation formula

13. Derive the regression lines of y on x and x on y?

OR14. Explain partial and multiple regression

15. Show that for n attributes (A1A2 …An) ≥ (A1) + (A2) + … + (An) – (n-1)N. where N is the total number of observations.

OR

16. Prove that in the usual notation Q = 2 y

1+ y2

17. Define chi – square variate. Write its probability density function. Mention the properties and applications of chi – square distribution.

OR

18. Obtain the relationship between t and F.

Soil temperature c0 49 57 42 40 38 42 45 42 44 40 46 44Germination time (hours)

29 10 26 30 41 29 27 27 19 18 19 31

Practical -III

1. Fitting of straight line by the method of least squares 2. Fitting of parabola by the method of least squares 3. Fitting of straight line and parabola by the method of least squares using MS Excel.4. Fitting of power curve of the type y=axb by the method of least squares.5. Fitting of exponential curve of the type y=aebx and y=abx by the method of least

squares. 6. Fitting of power curve and exponential curve of the type y=axb , y=aebx and y=abx by

the method of least squares using MS Excel 7. Computation of Yule's coefficient of association 8. Computation of Pearson's, Tcherprows coefficient of contingency 9. Computation of correlation coefficient and regression lines for ungrouped data 10. Computation of correlation coefficient, forming regression lines for ungrouped data11. Computation of correlation coefficient, forming regression lines for grouped data 12. Computation of correlation coefficient, forming regression lines using MS Excel13. Computation of multiple and partial correlation coefficients 14. Computation of multiple and partial correlation coefficients using MS Excel15. Computation of correlation ratio

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



Semester: IV paper: IV

Name of the Module: Statistical InferenceUnit – I

Estimation Theory: Point estimation of a parameter, concept of bias and mean square error of an estimate. Criteria of good estimator- consistency, unbiasedness, efficiency and sufficiency with examples. Statement of Neyman’s Factorization theorem, Estimation by method of moments, Maximum likelihood (ML), statements of asymptotic properties of MLE. Concept of interval estimation. Confidence intervals of the parameters of normal population

Unit – IITesting of Hypothesis: Concepts of statistical hypotheses, null and alternative hypothesis, critical region, two types of errors, level of significance and power of a test. One and two tailed tests, test function (non-randomized and randomized). Neyman-Pearson’s fundamental lemma for Randomized tests. Examples in case of Binomial, Poisson, Exponential and Normal distributions.

Unit – IIILarge sample Tests: large sample test for single mean and difference of two means, confidence intervals for mean(s). Large sample test for single proportion, difference of proportions. standard deviation(s) and correlation coefficient(s).

Unit – IVSmall Sample tests: t-test for single mean, difference of means and paired t-test. c2-test for goodness of fit and independence of attributes. F-test for equality of variances.

Unit – VNon-parametric tests- their advantages and disadvantages, comparison with parametric tests. Measurement scale- nominal, ordinal, interval and ratio. One sample runs test, sign test and Wilcoxon-signed rank tests (single and paired samples). Two independent sample tests: Median test, Wilcoxon –Mann-Whitney U test, Wald Wolfowitz’s runs test.

List of Reference Books:

1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand&Sons, New Delhi

2. Goon AM, Gupta MK,Das Gupta B : Outlines of Statistics , Vol-II, the World Press Pvt.Ltd., Kolakota.

3. Hoel P.G: Introduction to matehematical statistics, Asia Publiushing house.4. Sanjay Arora and Bansi Lal:.New Mathematical Statistics Satya Prakashan , New Delhi5. Hogg and Craig :Introduction to Mathematical statistics. Printis Hall6. Siegal,S.,and Sidney: Non-param etric statistics for Behavioral Science. McGraw Hill.7. GibbonsJ.D and Subhabrata Chakraborti: Nonparametric Statistical Inference. Marcel

Dekker.8. Parimal Mukhopadhyay: Mathematical Statistics. New Central Book agency.9. Conover : Practical Nonparametric Statistics. Wiley series.10. V.K.Rohatgi and A.K.Md.Ehsanes Saleh: An introduction to probability and statistics.

Wiley series.11. Mood AM,Graybill FA,Boe’s DC. Introduction to theory of statistics. TMH12. Paramiteya mariyu aparameteya parikshalu. Telugu Academy.13. K.V.S. Sarma: Statistics Made simple do it yourself on PC. PHI14. Gerald Keller: Applied Statistics with Microsoft excel. Duxbury. Thomson Learning15. Levin, Stephan, Krehbiel, Berenson: Statistics for Managers using Microsoft Excel.4th

edition. Pearson Publication.16. Hogg, Tanis, Rao. Probability and Statistical Inference. 7th edition. Pearson Publication.

Question paper pattern






Subject: Statistics Semester: IV Paper – IV : Statistical Inference

MODEL QUESTION PAPERSection – A

Answer any FIVE questions. Each question carry FIVE marks 5X5 = 25

1. What do you mean by point estimation? What are the properties of a good estimator?2. A random sample of size ‘n’ is drawn from a normal population N (µ, ø 2). Show that

sample mean is an unbiased estimator for µ.3. Define the following terms

(a) Hypothesis (b) level of significance (c) Power of the test4. Let P be the probability that a coin will be fall head in a single toss in order to test

H0: P = 12 against H1: P =

34 . The coin is tossed 5 times and H0 is rejected if more than 3

heads are obtained. Find the probability of type-I error and power of the test.5. Explain the general procedure for tests of significance?6. A random sample of 12 boys had the following I.Q’s:

105,73,102,101,88,93,98,108,104,78,110 and 116. Do the data support the assumption that the I.Q. of the population is 100?

7. Write advantages and disadvantages of non-parametric methods over parametric methods.

8. Explain one sample Run test for Randomness

Section - BAnswer any FIVE questions, each question carries equal marks. 5X10=50 Marks

9. Explain maximum likelihood method of estimation and state the properties of M.L. estimation

OR10. Discuss the concept of “Interval Estimation” and give a suitable illustration?

11. State and Prove Neyman – Pearson Lemma?OR

12. For the Poisson distribution with parameter λ, find best critical region with size α for

testing H0 : λ=λ0 against H1 : λ=λ1 ( λ1≠ λ0 )

13. Derive the test procedure for testing the equality of two population proportions in the case of large samples.

OR14. Random samples drawn from metro cities gave the following data relating to heights of

adult males:

City A City B

Mean height 67.42 67.25

Standard Deviation 2.58 2.5

Number of samples 1000 1200

(a) Is there any significant difference between means?

(b) Is there any significant difference between Standard deviations?

15. Describe the F-test procedure for the equality of variances of two populations.

OR

16. Explain χ2 test for goodness of fit.

17. Explain Sign test for paired samples.

OR18. Describe Median Test for independent samples.

Practical - IV

1. Large sample test for single mean 2. Large sample test for difference of means3. Large sample test for single proportion4. Large sample test for difference of proportions5. Large sample test for difference of standard deviations6. Large sample test for correlation coefficient7. Large sample tests for mean(s), propotion(s), standard deviations and correlation

coefficient using MS excel.8. Small sample test for single mean 9. Small sample test for difference of means 10. Small sample test for correlation coefficient11. Paired t-test(paired samples).12. Small sample tests for means(s), paired t-test and correlation coefficient using MS Excel 13. Small sample test for single variance(χ 2 - test ) 14. Small sample test for difference of variances(F-test)15. Small sample test for single and difference of variances using MS Excel 16. χ 2 - test for goodness of fit and independence of attributes17. χ 2 - test for goodness of fit and independence of attributes using MS Excel.18. Nonparametric tests for single sample(run test, sign test and Wilcoxon signed rank test) 19. Nonparametric tests for related samples (sign test and Wilcoxon signed rank test) 20. Nonparametric tests for two independent samples (Median test, Wilcoxon –Mann-

Whitney - U test, Wald - Wolfowitz' s runs test)

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


(w.e.f. 2016 – 2017)Semester: V

Paper – V: DESIGN OF EXPERIMENTS and SAMPLING THEORYNo. of Hours/week : 03 credits 3_______________________________________________________________________ Objective:

To enable the students to understand and apply the sampling procedures to different situations.

To focus on the design and analysis of variance techniques in the statistical field experiments.

UNIT – IDesign - Organization and execution of sample surveys - principle steps in sample survey - Pilot survey - principles of sample survey - sampling and non-sampling errors - advantages of sampling over complete census - limitations of sampling. Sampling from finite population - simple random sampling with and Without replacement - unbiased estimate of the mean, variance of the estimate of the mean finite population correction estimation of standard error from a sample - determination of sample size.

UNIT – IIStratified random sampling - properties of the estimates - unbiased estimates of the mean and variance of the estimates of the mean-optimum and proportional allocations - relative precision of a stratified sampling and simple random sampling - estimation of gain in precision in stratified sampling. Systematic sampling - estimate of mean and variance of the estimated mean - comparison of simple and stratified with systematic random sampling.

UNIT – IIIAnalysis of Variance - one-way, two-way classification (without interaction) Multiple range tests: Newman Keul's test- Duncan's multiple range test. Fundamental Principles of Experiments - Replication, Randomization and Local Control Techniques. Completely Randomized Design (CRD) and its analysis-Randomized Block Design (RBD) and its analysis. Missing plot technique-Meaning-Least square method of estimating single missing Observation in RBD.

UNIT – IVLatin Square Design(LSD) and its analysis. Estimation of single missing Observation in LSD. Factorial experiments - Definition 22 and 23 factorial experiments and their Statistical analysis.

Books for Study: 1. Kapoor, V.K. and Gupta, S.P. : Fundamentals of applied statistics, Sultan and Chand.

Books for Reference:

1. Des Raj (1976): Sampling theory, Tata McGraw Hill. 2. Daroga Singh & Chaudhary, F.S. (1986): Theory and Analysis of Sample Survey Desi

Wiley Eastern. 3. Sukhatme P.V. et al (1984): Sample survey methods and its applications, Indian Society

of Agricultural Statistics, New Delhi.

4. Murthy, M.N. (1967): Sampling theory and methods, Statistical Publishing Society, Calcutta.

5. Sampath S. (1999): Sampling theory and methods. New Age International Ltd. Engineering Updates.

6. Montgomery, D (1972) Design of Experiments, John Wiley and Sons.




Section A: Consisting of 10 questions, atleast two from each unit. Answer any five questions. Each question carries five marks. Total marks for Section A is 5x5 = 25.Section B: Consisting of 10 questions, atleast two from each unit. Answer any five questions. Each question carries ten marks. Total marks for Section B is 5x10 = 50.


(w.e.f. 2016 – 2017)Semester: V

Paper – V: DESIGN OF EXPERIMENTS and SAMPLING THEORY

Time : 3 hrs Model Question Paper Max Marks: 75----------------------------------------------------------------------------------------

Answer any FIVE questions. Each question carries FIVE marks. 5x5 = 25

1. What is “analysis of variance” and where it is used? And also give its assumption.2. A test was given to five students taken at random from the fifth class of three schools of a

town, the individual scores are School I : 9 7 6 5 8School II : 7 4 5 4 5School III : 6 5 6 7 6

Carry out the analysis of variance and state your conclusions.3. Explain the statistical analysis of CRD.4. Derive the expression to estimate the single missing plot in

R.B.D.5. Describe a Latin Square Design. Write down its layout.6. What is a sample survey? In what respects is it superior to a census survey?7. What is simple random sample? Mention the one the method of drawing a random

sample.8. Show that in SRSWOR E(s2 ¿= S2

9. Explain the method of stratified random sampling. Show that ( yst)(the estimate of population sample mean) is an unbiased estimate of population mean.

10. Define systematic sampling write its advantages and disadvantages.

Section –B

Answer any FIVE questions. Each question carries TEN marks. 5x10 = 50

1. Explain the principles of experimentation with suitable examples.2. Explain two way classification.3. Obtain the relative efficiency of RBD over CRD.4. Write down the statistical analysis of Latin square design.5. Explain statistical analysis of 22

factorial design.6. Explain the different sources of sampling and non-sampling errors.

7. In SRSWOR show that V ¿ ) = N−nNn

S2

8. Explain the proportional and optimum allocation in Stratified random sampling.9. If we ignore finite population correction then show

that V( yst)opt ≤ V( yst)prop ≤ V( yn)R

10. If the population consists of linear trend show that V( yst) ≤ V( ysys) ≤ V( yran)


(w.e.f. 2016 – 2017)Semester: V

Paper – VI Statistical Quality ControlNo. of Hours/week : 03 credits 2

Unit – IStatistical Techniques in Quality Control:

Uses and Limitations of Statistical Quality Control Process and Product Control, Control charts Role of Normal Distribution Basis of Control Charts (3σ – Control Limits)Control Charts for Variables:

Introduction – Control Charts for Variables Control Chart for Mean(x – chart), Control Chart for Range (R – Chart), Control Chart for Standard deviation or S – Chart.

Unit – IIControl Charts for Attributes:

Introduction – Control Chart for Fraction Defective (P Chart), P Chart for Fixed Sample Size, P – Chart for Varying Sample Size, Control Chart for Number of Defectives (np Chart) Control Chart for Number of Defects per Unit (C – Chart) Comparison of Control Charts for Variables Vs AttributesLimits and Measures in SQL:

Introduction, Specification Limits, Process Capability Index.

Unit – IIIAcceptance Sampling Plans:

Introduction – Sampling Inspection, 100% Inspection, Definition of Basic Terms of Acceptance Sampling, Operating Characteristic curve Characteristics of OC Curve, Rectifying Inspection Plans.

Unit – IVSingle and Double Sampling Plans:

Introduction, Types of Sampling Plans, Single Sampling Plan (SSP), Double Sampling Plan, Characteristics of a Good Sampling Plan Comparison of SSP and DSP.

List of reference books.

1. V.K.Kapoor and S.C.Gupta; Fundementals of Applied Statistics. Sultan Chand.2. Applied Statistics - Telugu Academy.3. R.C.Gupta:Statistical Quality Control.4. D.C.Montgomary: Introduction to Statistical Quality Control. Wiley 5. Parimal Mukhopadhyay : Applied Statistics . New Central Book agency

Question Paper Pattern:



Section A: Consisting of 10 questions, atleast two from each unit. Answer any five questions. Each question carries five marks. Total marks for Section A is 25.Section B: Consisting of 10 questions, atleast two from each unit. Answer any five questions. Each question carries ten marks. Total marks for Section B is 50.


(w.e.f. 2016 – 2017)Semester: V

Paper – VI: Statistical Quality Control Time : 3 hrs Model Question Paper Max Marks: 75

----------------------------------------------------------------------------------------Section-A

Answer any FIVE questions. Each question carries FIVE marks. 5X5 = 25 Marks

1. Explain the Chances and assigrable Casses of Variation.2. What are the Uses of Statistical Quality Control?3. Explain 3Sigma limits.4. What is ment by Specification limits and Tolerance limits?5. Draw C-Chart for the following data and comment on the state of Prove. No. of missing

rivets in Aircraft:7,15,13,18,10,14,13,10,20,11,22,156. Explain the need for sampling inspection.7. Explain Producer’s risk and Consumer’s risk in acceptance sampling.8. Derive the OC Curve of a Single Sampling Plan.9. What are the Characteristics of a Good Sampling Plan.10. Compare Single Sampling Plan and Double Sampling Plan.

Section-B Answer any FIVE questions. Each question carries TEN marks. 5x10 = 50 Marks

11. What is Control Chart? Explain the basic Principles under Lying the control Charts. Distinguish between charts for variables and charts for attributer.

12. Explain the Procedure of constructing x and R Charts.13. Explain the Procedure of constructing np-Chart and C-Chart.14. Explain the Procedure of constructing P-Chart.15. Explain Six Sigma. What is the Importance of Six Sigma.16. Define and explain the following terms.

a. Acceptance Quality Level (AQL)b. Lot Tolerance Percent Defective (LTPD)c. Average Ont going Quality (AOQ)d. Average 0nt going Quality Level (AOQL)e. Average Sample Number (ASN)

17. Explain the objective and construction Procedure of operative Characteristic Curve.18. What is Average Sample Number (ASN) and Average Total Inspection (ATI).Explain the

method of their calculation for single Sampling Plan. Why are ASN and ATI calculated?19. Suppose that N=2000, Sample single=50, Acceptance number C=2 and rejection

number=3, Construct a single Sampling Plan for the data. 20. Construct OC and AOQ Curves for the following Single Sampling Plans. (1) N=10, c=1 (2) N=50, c=2 (3) N=100, c=4 (4) N=200, c=8


(w.e.f. 2016 – 2017)Semester: VI

Paper – VII: ECONOMIC STATISTICSNo. of Hours/week : 03 credits 3

Unit – ITime Series:

Time Series and its components with illustrations, additive, multiplicative models. Determination of trend by least squares (Linear trend, panabolic trend only), moving averages methods, simple average method. Determination of seasonal indices by ratio to moving average, Ratio to trend and Link relative methods.

Unit – IIIndex numbers:

Concept, construction, uses and limitations of simple and weighted index numbers. Laspayer’s, Paasche’s and Fisher’s index numbers, Critenion of a good index number, problems involved in the construction of index numbers, Fisher’s ideal index numbers. Fixed and chain base index numbers. Cost of living index number and wholesale price index number. Base shifting, splicing and deflation of index numbers.

Unit – IIIOfficial Statistics:

Functions and organization of CSO and NSSO. Agricultural Statistics, area and yield statistics. National income and computation, utility and difficulties in estimation of national income.

Unit – IVVital Statistics:

Introduction, definition and uses of vital statistics, sources of vital specific death rate, standardized death rate, crude birth rate, age specific fertility rate, general fertility rate, total fertility rate, measurement of population growth, crude rate of natural increase – pearl’s vital index. Gross reproduction rate and net reproduction rate. Life tables, construction and uses of life tables and abridged life tables.

Text Books:1. V.K.Kapoor and S.C.Gupta; Fundementals of Applied Statistics. Sultan Chand.2. Applied Statistics - Telugu Academy.3. Parimal Mukhopadhyay : Applied Statistics . New Central Book agency



Paper-VII: Economic Statistics

Time:3 Hours Max.Marks:75

Section-A

Answer any FIVE of the following questions. Each question carries 5 Marks 5X5=25M

1. Define Time Series. Also write its Uses.2. Explain additive and Multiplicative models in Time Series.3. Explain the method of simple averages, to determine seasonal variations.4. Explain the Procedure to construct the cost of living index number.5. Explain fixed and Chain base index numbers.6. What are the main functions of central Statistical organization (CSO).7. Explain (a) Agricultural Statistics and (b) Yield Statistics.8. Define Vital Statistics and write its Uses.9. Define the rate of mortality also explain various death rates in Vital Statistics. 10. Explain abridged life table.

Section-B

Answer any FIVE of the following questions. Each question carries 10 Marks. 5X10=50M

11. Explain the least Square method of estimate the trend in time series analysis.12. Describe the measurement of seasonal variations by ratio-to-moving average . Method.13. Explain the Problems involved in the construction of Index numbers.14. Define Index Numbers. Explain various Weighted index numbers.15. Explain the tests of reversibility.16. Explain the computational procedure of National income.17. Explain in detail utility and difficulties in estimation of National Income.18. Explain various rates of fertility and write their merits and demerits.19. Explain the construction and Uses of life table.20. Explain the method of Link relatives to estimate the seasonal indices in Time Series Analysis.



Paper – VIII : LINEAR PROGRAMMING AND ITS APPLICATIONS No. of Hours/week : 04 credits 2

Unit – I

Introduction – Origin – Nature of OR – Structure – Characteristics – OR in Decision making – Models in OR – Phase of OR – Uses and Limitations of OR – LPP- Mathematical formulation of LPP – Graphical Method.

Unit – II

LPP – Standard form of LPP - Maximization – Minimization – Simplex method – Artificial variable technique – Big-M method – Two phase method.

Duality in LPP – Formulation of Dual LPP – Primal and Dual relationships(properties only) – Solving LPP using Dual concepts.

Unit – III

Transportation problem – Balanced, Unbalanced T.P. – Initial basic feasible solution – North West Corner Rule- Least Cost entry Methhod( Matrix minima) – Vogel’s approximation method – Optimum solution – MODI method.

Assignment problem – Introduction – Balanced – Unbalanced – Maximization – Minimization – Hungarian method.

Unit – IVSequencing problem – Problems with n-jobs on two machines – problems with n- jobs on

three machines – problems with n-jobs on m-machines.Reference Books:1. Kanti Swarup, P.K.Gupta, Manmohn (1980) – Operations Research, Sultan Chand and sons,

New Delhi.2. J.K. Sharma: (1997), Operations Research and Application, Mc.Millan and Company, New

Delhi.3. Nita H.Shah, Ravi M.Gor, Hardik Soni (2010)- Operations Research, PHI

Learning Private Limited, New Delhi. 4. Gass: Linear Programming. Mc Graw Hill. 5. Hadly : Linrar programming. Addison-Wesley.

6. Wayne L. Winston : Operations Research. Thomson, India edition. 4th edition.7. Taha : Operations Research: An Introduction : Mac Millan. 8. Parikriya Parishodhana - Telugu Academy.



Paper-VIII: Linear Programming and its ApplicationsTime:3 Hours Max.Marks:75

Section-A

Answer any FIVE of the following questions. Each question carries 5 Marks 5X5=25M

1. Define Linear Programming Problem and its applications.2. Explain the graphical method of solving an LPP involving two variables.3. Solve the following LPP by graphical method

Max Z = 6X1+X2

Subject to: 2X1+X2 ≥ 3 X1-X2 ≥ 0 X1, X2 ≥ 0

4. Explain the following terms. (1) Slack Variable (2) Surplus Variable (3) Standard form of LPP.

5. Show that dual of the dual is primal.6. Explain the least Cost entry method for obtaining an initial basic feasible

Solution of a T.P. 7. Find IBFS by Vogel’s approximation method.

D1 D2 D3 D4 SupplyS1 3 7 6 4 5S2 2 4 3 2 2S3 4 3 8 5 3Demand 3 3 2 2

8. What is an assignment Problem? Explain mathematical representation of Assignment problem.

9. Define the Problem of Sequencing and Explain its assumptions.10. We have five jobs each of which must go through the two machines A and B in the order

AB. Processing times in hours are given in the table below.

Job : 1 2 3 4 5 Machine A : 5 1 9 3 10

Machine B : 2 6 7 8 4 Determine the optional sequence that will minimize the elapsed Time.

Section-B

Answer any FIVE of the following questions. Each question carries 10 Marks. 5X10=50M

11. Explain the meaning, definition and scope of OR.12. A firm can produce 3 types of cloth, A, B and C. Three kinds of wool are required Red,

Green and Blue.1 unit of length of type A cloth needs 2 meters of red wool and 3 meters of blue wool. 1 unit of length of type B cloth needs 3 meters of red wool, 2 meters of green wool and 2 meters of blue wool.1 unit type of C cloth needs 5 meters of green wool and 4 meters of blue wool. The firm has a stock of 8 meters of red, 10 meters of green and 15 meters of blue. It is assumed that the income obtained from 1 unit of type A is Rs.3, from B is Rs.5 and from C is Rs.4. Formulate this as an LPP.

13. Solve the following LPP by using graphical method. Maximize Z=2X1+X2 Subject to X1+2X2≤10 X1+X2 ≤ 6 X1-X2≤ 2 X1-2X2≤ 1 And X1, X2 ≥ 014. Describe the Computational Procedure of the Simplex method for the solution of a maximization LPP.15. Explain Big-M Method.16. Use two Phase Simplex method to solve the following LPP. Maximize Z=3X1+2X2

Subject to: 2X1+X2 ≤ 2 3X1+4X2≥12 X1, X2 ≥ 0

17. Solve the following T.P.

Origins Destinations Supply/ Available D E F G

A 11 13 17 14 250B 16 18 14 10 300C 21 24 13 10 400

Demand/ requirement

200 225 275 250

18. Solve the following Assignment Problem.

Jobs PersonsP1 P2 P3 P4 P5

J1 3 8 2 10 3J2 8 7 2 9 7J3 6 4 2 7 5J4 8 4 2 3 5J5 9 10 6 9 10

19. Describe the method of Processing n ’jobs through three machines.

20. Determine the optional sequence of jobs that minimize the total elapsed time based on the following information Processing time on machines is given in hours and passing is not allowed.

Job : A B C D E F G M1 : 3 8 7 4 9 8 7 M2 : 4 3 2 5 1 4 3 M3 : 6 7 5 11 5 6 12

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