Sampling Distributions

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

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

 

CO 31:Ability to frame the hypothesis and  give inference through probability curve

 

CO 32: Analyse the behaviour of the data and also fit the appropriate sampling distributions on them.

 

CO 33: 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: 

1. Goon, A.M., Gupta, M.K. and Dasgupta, B. (1991): Fundamentals of Statistics,

    Volume II, The World Press Pvt Ltd, Calcutta

2. Gupta, S.C. and Kapoor, V.K. (2000): Fundamentals of Mathematical Statistics, S Chand & Company, New Delhi

References: 

1. Mood Alexander M., Graybill Frankline and Boes Duane C.(2007): Introduction to Theory

    of Statistics, McGraw Hill & Company Third Edition

2. Speigel M.R., (1967): Theory and Problem of Statistics, Schaum’s Publishing Series.

3. Gupta, O.P.:Mathematical Statistics, Kedarnath Publication, Meerut

4. Goon, A.M., Gupta, M.K. and Dasgupta, B. (2003): An Outline of Statistics Volume  

    II,The World Press Pvt Ltd, Calcutta

 

Academic Year: 
2020-2021
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