# STU22005 – Applied Probability II

## Module Learning Outcomes

On successful completion of this module, students will be able to:
LO1. Derive confidence intervals and hypothesis tests for means and variances.
LO2. Derive prediction intervals for simple statistical models and explain
how they differ from confidence intervals.
LO3. Conduct and explain the outputs of hypothesis testing in regression
analysis.
LO4. Define maximum likelihood estimates and how to compute them.
LO5. Implement a bootstrap to construct confidence intervals.
LO6. Construct appropriate graphs for assessing if data is normally distributed.

## Module Content

Recap of probability distributions.
Derivation of the confidence interval and tests of hypothesis for normal data.
The difference between a confidence interval and a prediction interval.
The Central Limit Theorem and what it says about confidence intervals and tests of hypothesis.
Hypothesis testing for regression analysis.
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 (2 hours, 100%)

## Contact Hours and Indicative Student Workload

George Casella, Roger L. Berger, Statistical Inference, 2nd Edition

Douglas C. Montgomery, George C. Runger, Norma F. Hubele, Engineering Statistics,
5th 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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