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# STA2302 Statistical Inference

 Semester 2, 2021 Online Short Description: Statistical Inference Units : 1 Faculty or Section : Faculty of Health, Engineering and Sciences School or Department : School of Sciences Student contribution band : Band 1 ASCED code : 010103 - Statistics Grading basis : Graded Version produced : 6 August 2021

## Staffing

Examiner: Shahjahan Khan

## Requisites

Pre-requisite: STA2301

## Rationale

Methods of Statistical Inference, where conclusions are drawn from data that are subject to random variation, form the basis of substantial decision making within and beyond the field of statistics. This course builds on the fundamentals of statistical principles and probability distributions which were first introduced in the Distribution Theory course. It covers the basic logic and underlying philosophy of inference and extends to estimation of parameters and hypothesis testing procedures. An understanding of the concepts and techniques of this course is highly desirable for a practitioner of statistics.

## Synopsis

This course provides the students with a firm grounding in the theory and methods of statistical inference and builds on the material covered in STA2301 Distribution Theory. Students will use a number of statistical procedures useful for both parametric and nonparametric inferences and learn different applications for both. Within this course students shall derive statistical procedures from first principles. Furthermore, both point and interval estimation as well as test of hypotheses under the classical framework are covered. The theoretical developments which are established in this course are supported by practical applications.

## Objectives

Upon successful completion of this course students should be able to:

1. Identify the principles, processes and methods of statistical inference.
2. Evaluate inferential problems for various statistical models.
3. Apply appropriate statistical models and methods for real life data analysis.
4. Communicate statistical inferences using appropriate terminology for expert and non-expert audiences.

## Topics

Description Weighting(%)
1. Sampling Distributions (chi-squared, t- and F- distributions); Central Limit Theorem 10.00
2. Estimation: properties of estimators, methods of maximum likelihood and moments, interval estimation, sample size determination 20.00
3. Hypothesis Testing: concepts, Type I and II errors, normal-based tests of proportions, means and variances, large and small samples, one and two samples, Neyman-Pearson Lemma, likelihood ratio tests, power of a test. 20.00
4. One-way analysis of variance: Concept, F-test, Kruskal-Wallis test 10.00
5. Regression: the linear model, matrix approach to ordinary least squares, inference in the linear model 20.00
6. Distribution-Free tests: concepts, one and two sample tests of location, goodness-of-fit tests 20.00

## Text and materials required to be purchased or accessed

ALL textbooks and materials available to be purchased can be sourced from USQ's Online Bookshop (unless otherwise stated). (https://omnia.usq.edu.au/textbooks/?year=2021&sem=02&subject1=STA2302)

Wackerly, DD, Mendenhall, W & Schaeffer, RL 2008, Mathematical statistics with applications, 7th edn, Duxbury, Boston.
All additional study material will be provided on the course StudyDesk.

## Reference materials

Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.
Larsen, RJ & Marx, ML 2017, An introduction to mathematical statistics and its applications, 6th edn, Prentice Hall, Englewood Cliffs.
Miller, I & Miller, M 2014, John E. Freund's Mathematical statistics with applications, 8th edn, Pearson, Boston.

Activity Hours
Assessments 42.00
Online Lectures 26.00
Online Tutorials 26.00
Private Study 78.00

## Assessment details

Description Marks out of Wtg (%) Due Date Notes
ASSIGNMENT 1 100 15 19 Aug 2021
ASSIGNMENT 2 100 15 16 Sep 2021
ASSIGNMENT 3 100 15 07 Oct 2021
PROBLEM SET 100 55 18 Oct 2021 (see note 1)

Notes
1. This assessment will include a written submission and an online viva voce via zoom. Full details will be available on the course Study Desk.

## Important assessment information

1. Attendance requirements:
It is the students' responsibility to participate appropriately in all activities and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.

2. Requirements for students to complete each assessment item satisfactorily:
To complete each of the assessment items satisfactorily, students must obtain at least 50% of the marks available for each assessment item.

3. Penalties for late submission of required work:
Students should refer to the Assessment Procedure http://policy.usq.edu.au/documents.php?id=14749PL (point 4.2.4)

4. Requirements for student to be awarded a passing grade in the course:
To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available for the course.

5. Method used to combine assessment results to attain final grade:
The final grades for students will be assigned on the basis of the aggregate of the weighted marks obtained for each of the summative assessment components (the examination and assignments) in the course.

6. Examination information:
There is no examination for this course.

7. Examination period when Deferred/Supplementary examinations will be held:
Deferred and Supplementary examinations will be held in accordance with the Assessment Procedure https://policy.usq.edu.au/documents/14749PL.

8. University Student Policies:
Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene University policies and practices. These policies can be found at http://policy.usq.edu.au.

## Other requirements

1. Computer, e-mail and Internet access:
Students are required to have access to a personal computer, e-mail capabilities and Internet access to UConnect. Current details of computer requirements can be found at http://www.usq.edu.au/current-students/support/computing/hardware.

2. Students can expect that questions in assessment items in this course may draw upon knowledge and skills that they can reasonably be expected to have acquired before enrolling in this course. This includes knowledge contained in pre-requisite courses and appropriate communication, information literacy, analytical, critical thinking, problem solving or numeracy skills. Students who do not possess such knowledge and skills should not expect the same grades as those students who do possess them.

Date printed 6 August 2021