# STU22005 – Applied Probability II

## Module Learning Outcomes

On successful completion of this module, students will be able to:

1. Derive and implement confidence intervals and hypothesis tests for means and variances;
2. Conduct and explain the outputs of hypothesis testing in regression analysis;
3. Define and compute maximum likelihood estimates;
4. Implement a bootstrap analysis to construct confidence intervals and perform hypothesis tests.

## Module Content

This module will cover a range of topics, including:

• Recap of probability distributions;
• Derivation of the confidence interval and tests of hypothesis for normal data;
• The Central Limit Theorem and what it says about confidence intervals and tests of hypothesis;
• Hypothesis testing for regression analysis;
• The difference between a confidence interval and a prediction interval;
• The bootstrap approach to confidence intervals and tests of hypothesis;
• Introduction to maximum likelihood estimation and computation;
• Graphical assessments of normality;
• Introduction to multivariate distributions.

## Teaching and Learning Methods

Lectures and laboratories.

## Reassessment Details

Examination (1.5 hours, 100%).

## Contact Hours and Indicative Student Workload

• George Casella, Roger L. Berger, Statistical Inference, 2nd Edition.
• Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, Introduction to Linear Regression Analysis, 5th Edition.

## Module Pre-requisites

Prerequisite modules: STU11002 and STU22004. Alternatively, STU12501, STU12502 and STU23501.

N/A

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