Introduction to Statistical Inference

PURPOSE
To teach student concepts and principles related to the application of statistical inference to real world data analysis problems.

LEARNING OUTCOMES

• Demonstrate an understanding of the fundamentals of estimation theory, with particular reference to: methods of point estimation, properties of estimators, and interval estimation; and understand and be able to implement mainstream statistical theory and methods for estimating parameters of an unknown population.
• Demonstrate an understanding of the fundamentals of Hypothesis Testing, with particular reference to: problems of hypothesis testing, testing simple hypotheses, statistical tests for means, variances and proportions, and statistical tests for comparing populations; and understand and be able to implement mainstream statistical theory and methods for testing hypotheses on parameters of an unknown population.
• Be capable of analytic thought and also of bringing together concepts, theory and methods from different areas of learning in order to solve problems; apply the appropriate statistical methods and statistical software to analyse data and interpret the results.
• Demonstrate the use of statistical principles and concepts, and the integration of knowledge from other disciplines, across real-world contexts.

CORE CONTENT

• Random samples.
• Method of Moments Estimation.
• Maximum Likelihood Estimation.
• Least Squares Estimation.
• Properties of Estimators: Consistent, Unbiased, Sufficient, Efficiency & Fisher Information.
• Confidence Intervals.
• Hypothesis testing concepts.
• Testing of simple hypotheses: Neyman-Pearson Lemma.
• UMP Tests.
• Likelihood Ratio Test.
• One and Two Sample tests for means, variances and proportions.
• Chi-Square Goodness of Fit test.
• Contingency Tables.