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Hypothesis Testing and Sampling Distributions
This paper aims to understand the concept of hypothesis and sampling distributions and its applications.
Students will be able to:
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Course |
Learning outcomes (at course level |
Learning and teaching strategies |
Assessment Strategies
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Paper Code |
Paper Title |
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STT-301 |
Sampling Distributions |
CO 29: Identify the behaviour of the sample and their distribution.
CO 30: Frame the hypothesis and give inference through probability curve
CO 31: Analyse the behaviour of the data and also fit the appropriate sampling distributions on them.
CO 32: Apply the applications of sampling distributions to the real-world problems.
CO 33: 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 |
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
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.
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.
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.
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.
- 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
SUGGESTED READINGS:
- 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
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
