This course is designed to enable students to develop rigorous theoretical and analytical competencies in statistical hypothesis testing, optimal test construction, likelihood-based inference, sequential analysis, and multivariate testing, with emphasis on problem formulation, optimality criteria, and interpretation of inferential results.
Course Outcomes (COs)
CO1
Formulate and analyze statistical hypothesis testing problems by identifying appropriate null and alternative hypotheses, critical regions, error probabilities, significance levels, p-values, and power functions.
(Aligned with Module 1)
CO2
Apply the Neyman–Pearson framework to construct optimal tests, including Most Powerful (MP), Uniformly Most Powerful (UMP), and Uniformly Most Powerful Unbiased (UMPU) tests for one-sided and two-sided hypotheses in exponential family distributions.
(Aligned with Module 1 & Module 2)
CO3
Evaluate likelihood-based and similarity-based testing procedures, including likelihood ratio tests and Neyman structure tests, and assess their properties in multiparameter settings.
(Aligned with Module 2)
CO4
Design and analyze sequential testing procedures using Sequential Probability Ratio Tests (SPRT), and compute and interpret Operating Characteristic (OC) and Average Sample Number (ASN) functions for standard distributions.
(Aligned with Module 3)
CO5
Perform multivariate hypothesis testing using Hotelling’s, Mahalanobis, and related statistics, and analyze their distributions and applications in one-sample and two-sample multivariate normal settings.
(Aligned with Module 4)
CO6
Critically interpret inferential results and justify the choice of testing procedures based on optimality, efficiency, and underlying distributional assumptions.
(Integrative outcome across all modules)
Cognitive Level Mapping (Bloom’s Taxonomy)
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Remember / Understand: CO1
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Apply / Analyze: CO2, CO3, CO4
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Evaluate: CO5, CO6