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.

 

Students will be able to:

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-401

Statistical Inference

CO 44: Conduct hypothesis test about population mean and proportion.

 

CO 45: Get basic theoretical knowledge about fundamental principles for statistical inference.

 

CO 46: Perform point estimation and interval estimation under a large variety of discrete and continuous probability models.

 

CO 47: Construct and interpret a confidence interval about the population and variances.

 

CO 48: Compare two or more population parameters using parametric and non-parametric 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                                                                                                                           

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                                                                                                                         

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                                                                                                                       

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

 

 

9.00

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                                                                                                                          

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.

 

References: 

SUGGESTED READINGS:

 

  • 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.

 

e-RESOURCES:

 

 

JOURNALS:

 

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association
  • Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
  • Statistics and Applications, Society of Statistics, Computer and Applications
  • Stochastic Modeling and Applications, MUK Publications and Distributions

 

Academic Year: 
2022-2023
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