Statistical Inference

Paper Code: 
24CSTT301
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

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

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24CSTT301

Statistical Inference

(Theory)

 

CO 23: Identify the components and concepts involved in hypothesis testing, 

CO 24: Apply the principles of Chi-square distribution to various statistical tests.

CO 25: Demonstrate an understanding of Student’s-t and Fisher’s-t distributions and apply them on data.

CO 26: Explain the properties of estimators and apply methods of estimation.

CO 27: Evaluate confidence intervals for parameters and apply Neyman-Pearson lemma and MP test in hypothesis testing scenarios.

CO 28: Contribute effectively in course-specific interaction.

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: 
Statistical Hypothesis

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 Distribution

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 and F Distribution

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 variances. 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.

 

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

 

Academic Year: 
2024-2025
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