Statistical Inference

Paper Code: 
CSTT 301
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This paper is designed to familiarize the students with concepts of statistical inference.

 

Students will be able to:

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

CSTT 301

Statistical Inference

 

CO 21: Apply the applications of sampling distributions to real-world problems.

 

 

CO 22: Get basic theoretical knowledge about fundamental principles for statistical inference.

 

CO 23: Perform point estimation and interval estimation under a large variety of discrete and continuous probability models.

 

CO 24: Construct and interpret a confidence interval about the population and variances.

 

CO 25: Transform different populations  in a normal distribution.

 

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

 

 

12.00
Unit I: 

Definitions of random sample, parameter and statistic, null and alternative hypothesis, simple and composite hypothesis, procedure of testing of hypothesis, level of significance, Type I and Type II errors, p-value, power of a test and critical region. Sampling distribution of a statistic, sampling distribution of sample mean, standard error of sample mean. 

12.00
Unit II: 

Chi-square: Definition, Derivation, Moments, Moment Generating Function, Cumulant Generating Function. Limiting and Additive property of Chi-square variates. Distribution of ratio of chi-square variates. Applications of Chi-square. Chi-square test for testing normal population variance, Test for goodness of fit, Contingency table and Test for independence of attributes, Yates correction for 2x2 contingency table conditions of Chi-square.

12.00
Unit III: 

t: Definition of Student’s-t and Fisher’s-t statistics and derivation of their distributions. Limiting property of t-distribution. Applications: Testing of single mean, Difference of two means, paired t-test and sample correlation coefficient.

F-distribution: Definition of Snedecor’s F-distribution and its derivation. Applications- Testing of equality of two variance. Relationship between ‘t’ , ‘F’ and  chi-square statistics.

 

12.00
Unit IV: 

Estimation: Parameter space, sample space, point estimation, requirement of a good estimator, consistency, unbiasedness, efficiency, sufficiency, Minimum variance unbiased estimators, Cramer-Rao inequality and its applications, Methods of estimation: maximum likelihood method and their properties.

 

12.00
Unit V: 

Interval Estimation: confidence intervals for the parameters of normal distribution, confidence intervals for difference of mean and for ratio of variances. Neyman-Pearson lemma and MP test: statements and applications. 

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: 
2023-2024
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