Statistical Inferences

Paper Code: 
STT 401
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
Objective: 

This paper is designed to familiarize the students with concept of statistical inference which include estimation theory.

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-401

Statistical Inference

CO 39: Able to conduct hypothesis test about population mean and proportion.

 

CO 40: Able to obtain the point estimator and interval estimator of the parameters.

 

CO 41: Able to construct and interpret a confidence interval about the population and variances.

 

CO 42: Students will learn to apply non - parametric test such as run test, sign test and median test.

Approach in teaching:

Interactive Lectures,

Group Discussion,

Classroom Assignment

Problem Solving Sessions

 

Learning activities for the students:

Assignments

Seminar

Presentation

Subject based  Activities

Classroom Quiz

Assignments

Class Test

Individual Presentation

 

10.00
Unit I: 
UNIT I

Large Sample Test of Significance: Testing of significance for attributes and variables, tests of significance for single mean, standard deviation and proportions, tests of significance for difference between two means, standard deviations and proportions.

 

8.00
Unit II: 
UNIT II

Theory of Estimation: Point Estimation: problems of point estimation, properties of a good point estimator- unbiasedness, consistency, efficiency & sufficiency.-factorization theorem (without proof) and it applications.

 

 

9.00
Unit III: 
UNIT III

Concept of mean square error, Minimum Variance Unbiased Estimation, Cramer Rao Inequality,  Rao-Blackwell Theorem (Without proof) and  Lehman scheffe theorm (Without proof). Idea of most powerful test, uniformly most powerful test, randomized and non randomized test.

 

9.00
Unit IV: 
UNIT IV

Methods of point estimation: Method of Maximum Likelihood and its properties of MLEs (without proof). Methods of Moments: Least Squares method. Interval Estimation: Concept, confidence interval, confidence coefficient, construction of confidence interval for population mean, variance, difference of population mean when standard deviation are known and unknown of Normal Distribution.

 

9.00
Unit V: 
UNIT V

Neyman Pearson Lemma and its application for finding BCR. BCR in case of Binomial, Poisson and of Normal and Exponential Populations. Non Parametric Tests: Definition merits and limitations, Sign test for univariate and bivariate distributions, Run test and Median test for small and large samples.

 

Essential Readings: 
  • Goon, A.M., Gupta, M.K. and Dasgupta, B. Das (1991): An Outline of Statistics, Volume II, The World Press Pvt Ltd, Calcutta
  • Gupta, S.C. and Kapoor, V.K.(2000): Fundamentals of Mathematical Statistics, S Chand & Company, New Delhi, tenth edition.
  • Mood Alexander M., Graybill Frankline and Boes Duane C.(2007): Introduction to Theory of Statistics, Mc Graw Hill & Company Third Edition
  • Rohatgi, V.K.(2009): An Introduction to Probability Theory and Statistics, John Wiley And Sons.
  • Casella, G. and Berger, Roger L.(2002): Statistical Inference, Duxbury Thompson Learning, Second Edition.
  • Snedecor, G.W. and Cochran, W.G. (1967): Statistical Methods, Iowa State University Press.
  • Rohatgi, V.K. and Saleh, A.K. Md. Ehsanes (2001): An Introduction to Probability Theory and Statistics, Second Edition, John Wiley and Sons.

 

Academic Year: 
2021-2022
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