Sampling Distributions

Paper Code: 
STT 301
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
Objective: 

This paper aims to understand the concept of hypothesis and sampling distributions and its applications.

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-301

Sampling Distributions

CO 26: Ability to Identify the behaviour of the sample and their distribution.

 

CO 27: Ability to frame the hypothesis and  give inference through probability curve

 

CO 28: Analyse the behaviour of the data and also fit the appropriate sampling distributions on them.

 

CO 29: Able to apply the applications of sampling distributions to the real-world problems.

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

 

7.00
Unit I: 
Basic Concepts:

Concept of statistic and sampling distribution. Sampling Distribution of sum of Binomial, Poisson and mean of Normal Distribution. Standard Error: Meaning and role. The Central Limit Theorem for identically independently distributed (i.i.d) random variable. 

10.00
Unit II: 
Statistical Hypothesis:

Definition, Simple and Composite hypotheses. Null and Alternative Hypotheses, procedure of testing, two Types of errors, critical region , level of significance critical and p-values, statistical test: one tailed and two tailed test, Power and size of the test.

 

10.00
Unit III: 
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.

 

10.00
Unit IV: 
t-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 test of sample correlation coefficient.

 

8.00
Unit V: 
F-Distribution:

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

 

Essential Readings: 
  • Goon, A.M., Gupta, M.K. and Dasgupta, B. (1991): Fundamentals 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
  • Mood Alexander M., Graybill Frankline and Boes Duane C.(2007): Introduction to Theory of Statistics, McGraw Hill & Company Third Edition
  • Speigel M.R., (1967): Theory and Problem of Statistics, Schaum’s Publishing Series.
  • Gupta, O.P.:Mathematical Statistics, Kedarnath Publication, Meerut
  • Goon, A.M., Gupta, M.K. and Dasgupta, B. (2003): An Outline of Statistics Volume  II,The World Press Pvt Ltd, Calcutta

 

Academic Year: 
2021-2022
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