Statistical Inference

Paper Code: 
25CSTT301
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 Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

25CSTT301

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: 
2025-2026
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