Programme Learning Outcomes in B.Sc. Statistics The student graduating with the Degree B.Sc. Statistics should be able to: 1. Demonstrate the ability to use Statistics knowledge to identify and apply appropriate methodologies to solve a wide range of problems associated with Statistics. 2. Plan and execute Statistical experiments or investigations, analyze and interpret data collected using appropriate methods and appropriate statistical software, and prepare a report of the findings of the experiment/investigations. 3. Find employment utilizing his/her appropriate statistical skill in interdisciplinary areas such as finance, insurance, health, agriculture, government, business, industry, telecommunication, and bio-statistics. Consequently, they can pursue their future career either in the core field or in the applied field of Statistics. 4. Use his/her appropriate statistical skill in interdisciplinary areas such as finance, health, agriculture, government, business, industry, telecommunication, and bio-statistics. As a result, they can pursue their future career either in the core field or in the applied field of Statistics.
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Programme Learning Outcomes in B.Sc. Statistics 1. 2. 3. 4....SARDAR PATEL UNIVERSITY B.SC. SYLLABUS STATISTICS SEMESTER – III Effective from June, 2019 Sr. No. Course code Title
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Programme Learning Outcomes in B.Sc. Statistics
The student graduating with the Degree B.Sc. Statistics should be able to:
1. Demonstrate the ability to use Statistics knowledge to identify and apply appropriate
methodologies to solve a wide range of problems associated with Statistics.
2. Plan and execute Statistical experiments or investigations, analyze and interpret data
collected using appropriate methods and appropriate statistical software, and prepare a
report of the findings of the experiment/investigations.
3. Find employment utilizing his/her appropriate statistical skill in interdisciplinary areas
such as finance, insurance, health, agriculture, government, business, industry,
telecommunication, and bio-statistics. Consequently, they can pursue their future career
either in the core field or in the applied field of Statistics.
4. Use his/her appropriate statistical skill in interdisciplinary areas such as finance, health,
agriculture, government, business, industry, telecommunication, and bio-statistics. As a
result, they can pursue their future career either in the core field or in the applied field of
Statistics.
SARDAR PATEL UNIVERSITY
B.SC. SYLLABUS
STATISTICS
SEMESTER – III
Effective from June, 2019
Sr. No. Course code Title of the paper
Credit Lecture per week/batch
Core/Skill Enhancement
1 US03CSTA21 Descriptive Statistics
4 4 Core
2 US03CSTA22 Elements of Probability
Theory
4 4 Core
3 US03CSTA23 Statistics Practical - I
4 8 Core
4 US03SSTA21 Foundation of Statistics - I
2 2 Skill Enhancement
5 US03SSTA22 Operations Research-I
2 2 Skill Enhancement
6 US03SSTA23 Biostatistics - I 2 2 Skill Enhancement
SARDAR PATEL UNIVERSITY
Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science)
(B. Sc.) (Statistics) Semester (III)
Course Code US03CSTA51
Title of the
Course DESCRIPTIVE STATISTICS
Total Credits
of the Course 04
Hours per
Week 04
Course
Objectives:
1. To understand the purpose of descriptive statistics
2. To compute various measures of central tendency, dispersion with its
merits and demerits and its usefulness in real life.
3. To explain the problems arising in the construction of index numbers,
importance of an index numbers.
4. To perform basic demographic analyses using various techniques.
5. To learn the main theories used to understand population studies.
Course Content
Unit Description Weightage*
(%)
1. Analysis of Quantitative data - I
Types of data : Quantitative data : Discrete and Continuous,
Qualitative data : Nominal and Ordinal
Measures of central tendency : Mean, Median, Mode, Geometric mean,
method, Properties of correlation coefficients ( without proof),
Applications,
Regression: Meaning, Properties of regression coefficients (without
proof), Applications
25
2. Continuous Probability distribution: Normal distribution, Definition,
Properties (without proof), Area under normal curve, Applications 25
3. Test of Significance – I: Test of independence, Large sample test: test
for population proportion, test for difference between two population
proportions, test for population mean, test for difference between two
population means
25
4. Test of Significance – II: Small sample test: test for population mean,
test for difference between two population means (Unpaired t - test),
test for difference between two population means (Paired t - test) 25
SARDAR PATEL UNIVERSITY
Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 2 of 3
Teaching-
Learning
Methodology
Evaluation Pattern
Sr.
No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce,
Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. learn how to apply linear regression models in practice
2. understand and interpret the correlation between two variables
3. understand and use of normal distribution in real life.
4 use the concepts of testing of hypotheses, large and small sample test.
Suggested References:
Sr.
No.
References
1. Gupta S.C. : Mathematical Statistics
2. Mahajan B.K. : Methods in Biostatistics
3 Sancheti D.C. and Kapoor V.K. : Statistics
SARDAR PATEL UNIVERSITY
Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 3 of 3
4 Wayne W. Daniel: Biostatistics - A foundation for analysis in the health sciences
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY B.Sc. Statistics New CBCS
Semester - V (Effective From June 2020)
Sr. No. Subject Code Subject Name Credit 1 US05CSTA21 Mathematical Statistics 4 2 US05CSTA22 Theory of estimation 4 3 US05CSTA23 Survey sampling 4 4 US05CSTA24 Statistical quality control 4 5 US05CSTA25 Statistics Practicals 6 6 US05DSTA26 Statistical data analysis using software
packages 2
Total Credits 24
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (V)
Course Code US05CSTA51 Title of the
Course MATHEMATICAL STATISTICS
Total Credits of the Course 04 Hours per
Week 04
Course Objectives:
1. To understand the key concepts in probability and distribution theory 2. To understand the concepts of various inequalities, law of large
numbers 3. To learn various discrete probability distributions as a particular case of
power series distribution 4. Large sample results such as the central limit theorem will be used to
approximate a sampling distribution 5. To learn various continuous probability distributions 6. Emphasis is placed on theoretical understanding combined with
problem solving.
Course Content
Unit Description Weightage* (%)
1. Probability: Probability of union of 𝑛𝑛 events, Boole’s inequality, Bonferroni’s inequality, convergence in probability and in distribution, Chebychev’s inequality, Weak law of large numbers, Characteristic function and its properties (without proof)
25
2. General statement of Central Limit Theorem (CLT), Lindberg Levy form, Statement of Liapunov form (without proof). Applications of Central Limit Theorem (CLT).
25
3. Power Series Distributions:
Definition, p.g.f and m.g.f. of PSD, the recurrence relations between raw moments and central moments of PSD. The results of known discrete distributions as particular cases. Truncated Binomial and Truncated Poisson distributions (truncated at 𝑋𝑋 = 0)
25
4. Continuous Probability Distributions:
Lognormal, Cauchy, Laplace and Weibull distributions. Moments and their relations. Incomplete Gamma and incomplete Beta distributions
25
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Page 2 of 3
as tail probabilities of Poisson and Binomial distributions. Truncated Normal distribution (Truncated at left)
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. learn key concepts of probability and probability distributions
2. learn central limit theorem and its applications in understanding the concepts of statistical inference.
Suggested References:
Sr. No.
References
1. Dudewic and Misra: Modern Mathematical Statistics, John Wiley & Sons.
2. Mukhopadhyay, P.(2006): Mathematical Statistics, 3ed., Books abd Allied(P) Ltd.
3 Rohatgi, V.K. & A.K. Md.E. Saleh (2001): An Introduction to Probability and Statistics, John Wiley (2nd Edition)
4 Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, Sultan
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 3 of 3
Chand and Sons
5 Hogg, Mckean and Craig : Introduction to Mathematical Statistics, 8th edition
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (V)
Course Code
US05CSTA52 Title of the
Course THEORY OF ESTIMATION
Total Credits of the Course
04 Hours per
Week 04
Course Objectives:
1. To learn the concepts of point estimation , methods including method of moments and maximum likelihood, bias and variance, mean squared error, sufficiency, completeness, the Cramer – Rao inequality, uniformly minimum variance unbiased estimators.
2. Confidence intervals construction methods, including likelihood based intervals, inversion methods, intervals based on pivots.
Course Content
Unit Description Weightage* (%)
1. Point Estimation – I
Estimation: Concepts of estimation, unbiasedness, consistency and efficiency. Rao – Cramer inequality, Fisher’s information, Minimum Variance Bound Unbiased Estimators (MVBUE).
25
2. Sufficiency: Fisher Neyman factorization criterion (theorem) (for one parameter discrete distributions with proof and for continuous distributions without proof).
25
3. Point Estimation – II
Methods of Estimation:
Methods of moments, method of maximum likelihood. Properties of maximum likelihood estimation (Without proof). Method of iteration for maximum likelihood estimators (Method of scoring)
25
4. Interval estimation:
Random interval, definition of confidence interval, confidence intervals for the parameters of a normal distribution, for difference of two normal means, for ratio of two normal variances, for binomial
25
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(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 2 of 3
proportion and for difference of two binomial proportions.
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. explain in detail the notion of a parametric model and point estimation of the parameters of those models.
2. explain in detail and demonstrate approaches to include a measure of accuracy for estimation procedures and our confidence in them by examining the area of interval estimation.
Suggested References:
Sr. No.
References
1. Hogg, R.V., Tanis, E.A. and Rao J.M. (2009): Probability and Statistical Inference, Seventh edition, Pearson Education, New Delhi
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2. Miller, Irwin and Miller, Marylees (2006): John E. Freund’s Mathematical Statistics with applications, (7th Edition), Pearson Education, Asia
3 Dudewic and Misra: Modern Mathematical Statistics, John Wiley & Sons.
4 Hogg, R.V. and Craig, A.T. (1972): Introduction to Mathematical Statistics, Amerind Publishing Co.
5 Lehmann, E.L. (1983): Theory of Point Estimation, Wiley Eastern
6 Robert V. Hogg and Elliot Tanis : Probability and Statistical Inference, 8th edition
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (V)
Course Code
US05CSTA53 Title of the
Course SURVEY SAMPLING
Total Credits of the Course
04 Hours per
Week 04
Course Objectives:
1. To introduce the basic concepts of survey sampling theory including brief introduction to questionnaire design, methods of sample selection, estimation, sampling variance, standard error of estimation in finite population
2. Development of sampling theory for use in sample survey problems and sources of errors in surveys.
3. Practical examples will be used to illustrate the principles and methods.
Course Content
Unit Description Weightage* (%)
1. Basics of Survey sampling and Equal Probability Sampling Scheme:
Concept of population and sample, Complete enumeration V/S sampling. Basic principles of sample survey.
Simple Random Sampling (SRS) with and without replacement, definition and procedure of selecting a random sample, estimates of population mean, total and proportion, variances of these estimates, estimates of their variances.
25
2. Stratified Random Sampling: Technique, estimates of population mean and total, variances of these estimates, proportional and optimum allocations and their comparison with SRS. Practical difficulties in allocation.
25
3. Systematic sampling: Technique, estimates of population mean and total, variances of these estimates (𝑁𝑁 = 𝑛𝑛𝑛𝑛). Comparison of systematic sampling with SRS and stratified random sampling.
25
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(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 2 of 3
4. Determination of sample size: Determination of sample size for proportion and continuous data in case of SRS. Cluster sampling (Equal clusters only) (Introduction only)
Sampling and non – sampling errors.
25
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. understand and interpret real life survey reports
2. understand concepts and techniques in sampling methods
3. understand solution methodology to estimate population parameters
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 3 of 3
2. Sukhatme, P.V., Sukhatme, B.V.: Sampling Theories of Survey With Application, IOWA State University Press and Indian Society of Agricultural Statistics
4 Gupta, S.C. And Kapoor, V.K. (2005): Fundamentals of Applied Statistics, Sultan Chand & Sons
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (V)
Course Code
US05CSTA54 Title of the
Course STATISTICAL QUALITY CONTROL
Total Credits of the Course
04 Hours per
Week 04
Course Objectives:
1. To understand the concepts underlying statistical quality control 2. To develop ability to apply those concepts to the design and
management of quality control processes in industries 3. To apply statistical tools to analyze, design and use of various charts for
quality control
Course Content
Unit Description Weightage* (%)
1. Quality:
Definition, dimensions of quality, Quality system and standards. Introduction to ISO quality standards, Quality registration.
Statistical Process Control (SPC), chance and assignable causes of quality variation.
25
2. Statistical quality control charts:
Construction and statistical basis of 3𝜎𝜎 control charts.
Control charts for variable: X – bar & R chart, X – bar and S chart.
Control charts for attribute: 𝑝𝑝 – chart, 𝑛𝑛𝑝𝑝 chart, 𝐶𝐶 chart and 𝑢𝑢 chart. Comparison between control charts for variables and attributes.
25
3. Acceptance sampling plan:
Principles of acceptance sampling plans. Single sampling plan their OC, AQL, LTPD, AOQ, AOQL, ASN and ATI functions with graphical interpretations.
25
4. Double sampling plans their OC, AQL, LTPD, AOQ, AOQL, ASN and ATI functions.
25
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 2 of 3
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. understand the basic concepts of quality, quality control and tools to improve quality
2. demonstrate the ability to use and interpret control charts for variables and attributes understand the concepts of various acceptance sampling plans
3. understand the concepts of various acceptance sampling plans
Suggested References:
Sr. No.
References
1. Montogomery, D.C. (2009): Introduction to Statistical Quality Control, 6th Edition, Wiley India Pvt. Ltd.
2. Mukhopadhyay, P (2011): Applied Statistics, 2nd Edition revised reprint, Books and Allied (P) Ltd.
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
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Page 3 of 3
3 Gupta, S.C. And Kapoor V.K.(2005): Fundamentals of Applied Statistics, Sultan Chand & Sons
4 Chapman and Hall, - Brownlee, K.A.(1960): Statistical Theory and Methodology in Science and Engineering, john Wiley & Sons.
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (V)
Course Code
US05DSTA56 Title of the
Course STATISTICAL DATA ANALYSIS USING SOFTWARE PACKAGES
Total Credits of the Course
02 Hours per
Week 02
Course Objectives:
1. To understand the basic concepts of loading data, plotting graph, generating different descriptive statistical measures, correlation and regression analysis using statistical softwares
2. To generate random numbers and understand the concepts of fitting of polynomials and exponential curves and normal probability plot using statistical softwares
3. To learn to do simple analysis and create and manage statistical analysis and understand the concepts of hypotheses testing.
Course Content
Unit Description Weightage* (%)
1. Learn how to load data, plot a graph viz. histograms (equal class intervals and unequal class intervals), Box – plot, Stem – leaf, frequency polygon, pie chart, ogives with graphical summaries of data.
3. Random number generation and sampling procedures. Fitting of polynomials and exponential curves. Application problems based on fitting of suitable distribution. Normal probability plot.
25
4. Simple analysis and create and manage statistical analysis projects, import data, code editing, Basics of statistical inference in order to understand hypotheses testing and compute p – values and confidence intervals.
25
Teaching-
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 2 of 3
Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. do graphical presentation, fitting of various curves and hypotheses testing based on given data and is able to do statistical analysis of the data.
Suggested References:
Sr. No.
References
1. Moore, D.S. and McCabe, G.P. and Craig, B.A. (2014): Introduction to Practice of Statistics, W.H.Freeman.
2. Cunningham, B.J. (2012): Using SPSS: An Interactive Hands on approach.
On-line resources to be used if available as reference material
On-line Resources
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 3 of 3
*****
SARDAR PATEL UNIVERSITY B.Sc. Statistics New CBCS
Semester - VI (Effective from June – 2020)
Sr. No. Subject Code Subject Name Credit 1 US06CSTA21 Sampling distributions 4 2 US06CSTA22 Testing of hypothesis 4 3 US06CSTA23 Design of experiments 4 4 US06CSTA24 Operations Research 4 5 US06CSTA25 Statistics Practicals 6 6 US06DSTA26 Introduction to R programming 2
Total credits 24
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (VI)
Course Code
US06CSTA51 Title of the
Course SAMPLING DISTRIBUTIONS
Total Credits of the Course
04 Hours per
Week 04
Course Objectives:
1. To understand the concepts of sampling distributions and their applications in statistical inference
2. To learn bivariate normal distribution and its applications 3. To learn the concepts of order statistics applicable in understanding the
concepts of non - parametric tests
Course Content
Unit Description Weightage* (%)
1. Sampling distributions:
Distribution of function of one and two random variables. Distribution function technique, change of variable techniques, m.g.f and characteristic function techniques.
25
2. Exact sampling distribution - I
Chi – square distribution: Definition and derivation of pdf of 𝜒𝜒2 with 𝑛𝑛 d.f. using m.g.f technique, nature of pdf curve for different degrees of freedom, mean, variance, m.g.f ,c.g.f., additive property and limiting form of 𝜒𝜒2 distribution.
25
3. Exact sampling distribution – II:
t – distribution: Student’s t and Fisher’s t – distribution, derivation of its pdf, nature of pdf curve with different degrees of freedom, mean, variance, moments and limiting form of t – distribution. F – distribution: Snedecor’s F – distribution, derivation of pdf, nature of curve with different degrees of freedom, mean, variance. Distribution of ratio of F – distribution.
25
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4. Bivariate Normal distribution:
Bivariate normal distribution as a particular case of multivariate normal distribution. Distribution of sample correlation coefficient 𝑟𝑟.
Order statistics: Definition: distribution of 𝑟𝑟𝑡𝑡ℎ order statistics. Joint pdf of 𝑟𝑟𝑡𝑡ℎand 𝑘𝑘𝑡𝑡ℎ order statistics. Distribution of sample range and sample median (for continuous distribution only)
25
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. derive probability distributions of functions of one and two variables using various techniques like m.g.f, distribution function and change of variable.
2. derive probability distributions of various sampling distributions like chi square, t and F distributions applicable in understanding the concept of testing of hypotheses
Suggested References:
Sr. References
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 3 of 3
No.
1. Dudewic and Misra: Modern Mathematical Statistics, John Wiley & Sons.
2. Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, Sultan Chand and Sons
3 Mukhopadhyay, P.(2006): Mathematical Statistics, 3ed., Books abd Allied(P) Ltd.
4 Rohatgi, V.K. & A.K. Md.E. Saleh (2001): An Introduction to Probability and Statistics, John Wiley (2nd Edition)
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
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(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (VI)
Course Code
US06CSTA52 Title of the
Course TESTING OF HYPOTHESIS
Total Credits of the Course
04 Hours per
Week 04
Course Objectives:
Hypothesis testing methods, including likelihood ratio tests, the Neyman – Pearson lemma and uniformly most powerful tests, power calculations, Bayesian approaches and non – parametric approaches.
Course Content
Unit Description Weightage* (%)
1. Principles of Test of significance:
Null and alternative hypotheses (Simple and composite), Type – I and Type – II errors, critical region, level of significance, size and power, Best critical region, Most powerful (MP) test, Uniformly Most Powerful (UMP) Test, Neyman Pearson lemma (Statement and applications to construct most powerful test).
25
2. Likelihood Ratio (LR) test, Properties of LR test (without proof). Applications of LR test (𝑖𝑖) mean and variance of normal distribution (𝑖𝑖𝑖𝑖) equality of variances of two independent normal distributions
25
3. Sequential Analysis:
Sequential Probability Ratio Test (SPRT) for simple v/s simple hypotheses. Determination of stopping bounds 𝐵𝐵 and 𝐴𝐴. OC and ASN functions of SPRT.
25
4. Non - Parametric Tests:
One sample and two sample sign test. Wald – Wolfwitz run test, Run test for randomness, Median test, Wilcoxon – Mann – Whitney test.
25
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Page 2 of 3
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. demonstrate the plausibility of pre – specified ideas about the parameters of the models by examining the area of hypothesis testing
2. explain in detail and demonstrate the use of non – parametric statistical methods.
Suggested References:
Sr. No.
References
1. Ross, S.M.: Introduction to Probability and Statistics for Engineers and Scientists, Elsevier
2. Dudewic and Misra: Modern Mathematical Statistics, John Wiley & Sons.
3 Hogg, R.V. and Craig, A.T. (1972): Introduction to Mathematical Statistics, Amerind Publishing Co.
4 Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, Sultan
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
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Chand and Sons
5 Robert V. Hogg and Elliot Tanis : Probability and Statistical Inference, 8th edition
On-line resources to be used if available as reference material
On-line Resources
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SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (VI)
Course Code
US06CSTA53 Title of the
Course DESIGN OF EXPERIMENTS
Total Credits of the Course
04 Hours per
Week 04
Course Objectives:
1. To learn how to plan, design and conduct experiments efficiently and effectively and analyze the data to obtain objective conclusions
2. Understanding the process of designing an experiments
Course Content
Unit Description Weightage* (%)
1. One Way Analysis of Variance and Completely Randomized Design (CRD)
For fixed effect model one way classification – Purpose and Analysis with equal number of observations per cell using ANOVA technique.
Concept of treatment, plot, block, yield, shapes and sizes of plots and blocks. Principles of experimental design: Randomization, Replication and Local Control.
Complete Randomized Design (CRD) – Introduction, Layout, Statistical analysis and its merits and demerits.
25
2. Two way Analysis of Variance and Randomized Block Design (RBD)
Two way classification – Purpose and Analysis with equal number of observations per cell using ANOVA technique – Expected values of sum of squares for both one way and two way classifications.
Randomized Block Design (RBD) – Introduction, layout, Statistical analysis and its merits and demerits.
Estimation of one and two missing yields. Efficiency of RBD over CRD.
25
3. Latin Square Design (LSD) : Introduction, layout, Statistical analysis and its merits and demerits. 25
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
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Estimation of one and two missing yields. Efficiency of LSD over RBD and CRD.
4. Factorial Experiments: Factorial experiments upto four factors each at two levels. Concept of confounding and their types. Confounding upto two interactions. Analysis of confounded factorial experiments.
25
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. appreciate the advantages and disadvantages of a design for a particular experiment
2. construct optimal or good designs for a range of practical experiments
3. understanding the potential practical problems in its implementation describe how the analysis of the data from the experiment should be carried out.
Suggested References:
Sr. No.
References
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
2. Montogomery D.C. (1976): Design and Analysis of Experiments, John Wiley
3 Cochran W.G. & Cox G.M.: Experimental Designs, John Wiley
4 Mukhopadhyay P. (1999): Applied Statistics
5 Federer W.T. (1975): Experimental Designs – Theory and Application, Oxford & IBH.
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
(Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (VI)
Course Code
US06CSTA54 Title of the
Course OPERATIONS RESEARCH
Total Credits of the Course
04 Hours per
Week 04
Course Objectives:
1. To impart knowledge in concepts and tools of Operations Research 2. To formulate verbal problem into mathematical form 3. To understand mathematical tools that are needed to solve optimization
problems used in Operations Research 4. To apply techniques constructively to make effective business
decisions.
Course Content
Unit Description Weightage* (%)
1. Linear Programming Problem (LPP), Mathematical formulation of LPP, Graphical solutions of a LPP. Simplex method for solving LPP. Special cases of LPP. Concept of duality in LPP, Dual simplex method.
25
2. Transportation Problem (TP): Initial solution by North – West corner rule, Least cost method and Vogel’s approximation method (VAM), Modi’s method to find the optimum solution, special cases of transportation problem.
Assignment Problem: Hungarian method to find optimal assignment, special cases of assignment problem.
25
3. Game Theory: Rectangular game, minimax – maximin principle, solutions to rectangular game using graphical method, dominance property to reduce the game matrix and solution to rectangular game with mixed strategy.
25
4. PERT and CPM: Project planning with PERT and CPM: Drawing of Project network, critical path identification, slack time and float. Calculation of probability of completing project within a specified
25
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 2 of 3
time.
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. solve Linear Programming problems
2. solve Transportation and Assignment Problems
3. understand the usage of game theory and network analysis.
Suggested References:
Sr. No.
References
1. KantiSwarup, Gupta R.K. and Manmohan (2007): Operations Research, 13th Edition, Sultan Chand and Sons.
2. Taha, H.A. (2007): Operations Research: An Introduction, Prentice Hall of India.
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 3 of 3
3 Heardly, G. (1962): Linear Programming
On-line resources to be used if available as reference material
On-line Resources
*****
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 1 of 3
((Bachelor of Science in Statistics) (Bachelor of Science) (B. Sc.) (Statistics) Semester (VI)
Course Code
US06DSTA56 Title of the
Course INTRODUCTION TO R
PROGRAMMING Total Credits of the Course
02 Hours per
Week 02
Course Objectives:
This course introduces the statistical computing language R (open source and free software) for under graduate students with no prior background in R or programming.
Course Content
Unit Description Weightage* (%)
1. Introduction to R: R as a Statistical Software and language, R preliminaries, methods of data input, Data accessing or indexing, Data frames and lists, Functions, Graphics with R, Saving, storing and retrieving work, work space and files, using scripts, using packages.
Descriptive Statistics Using R: Diagrammatic and graphical representation of data, Measures of central tendency, dispersion, skewness and kurtosis, selection of representative samples.
25
2. Probability and Probability distributions using R:
Probability : definition and properties, probability distributions, some special discrete distributions (Binomial, Poisson), Continuous probability distributions, some special distributions(Normal, Exponential)
Methods for generating random variables: Introduction, Random generation of common probability distribution in R, the inverse method, the acceptance and rejection methods, transformation methods
25
3. Correlation and Regression analysis: Correlation, correlation coefficient, Linear Regression, inference procedure for simple linear model, validation of linear regression model. Monte Carlo estimation and standard error. Estimation of MSE, estimating a confidence interval, Monte Carlo methods for hypothesis test, Empirical type – I
25
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 2 of 3
error, Power of a test, Comparison of powers of two tests
4. Statistical Inference: Sampling distribution of the sample mean, Estimation of parameters, plots to check normality, Hypothesis testing, Goodness of fit, One way and Two way ANOVA
25
Teaching-Learning Methodology
Evaluation Pattern
Sr. No.
Details of the Evaluation Weightage
1. Internal Written / Practical Examination (As per CBCS R.6.8.3) 15%
2. Internal Continuous Assessment in the form of Practical, Viva-voce, Quizzes, Seminars, Assignments, Attendance (As per CBCS R.6.8.3)
15%
3. University Examination 70%
Course Outcomes: Having completed this course, the learner will be able to
1. understand the basic concepts such as data type and index and use them in their work
2. demonstrate the use of basic functions
3. create their own customized functions
4 construct tables and graphs for descriptive statistics
5 import, review, manipulate and summarize data sets in R
6 explore data sets to create testable hypotheses and identify appropriate statistical tests
7 perform appropriate statistical test using R
SARDAR PATEL UNIVERSITY Vallabh Vidyanagar, Gujarat
(Reaccredited with ‘A’ Grade by NAAC (CGPA 3.25) Syllabus with effect from the Academic Year 2021-2022
Page 3 of 3
8 create and edit visualization with R.
Suggested References:
Sr. No.
References
1. Chambers J.M. (1998) : Programming with Data: A guide to S language, Springer
2. Statistics Using R – Purohit, S.G., et al. (2008), Narosa Publishing House
3 Statistical Computing with R – Rizzo, M.L. (2007), Chapman & Hall / CRC
On-line resources to be used if available as reference material