37151 Introduction to Statistics
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Subject handbook information prior to 2020 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Anti-requisite(s): 33116 Statistical Design and Analysis AND 33230 Mathematical Modelling 2 AND 33290 Statistics and Mathematics for Science AND 35151 Introduction to Statistics
Description
This subject gives an introduction to probability theory and statistics. Students learn how to describe random phenomena using the language of probability, and how this is applied in a statistical framework to solve real world problems. The first half of the subject introduces the students to important concepts in probability, such as random variables and their probability distributions. Fundamental properties such as expectations, independence and the Central Limit Theorem are discussed. The second half of the course introduces classical statistical inference and its connection to probability theory. Sampling distributions and their use in constructing confidence intervals and hypothesis testing are discussed. The course ends by introducing simple linear regression and analysis of variance techniques.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | understand how to use descriptive statistics to properly summarize a dataset; |
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| 2. | understand basic properties of random variables and their probability distributions; |
| 3. | determine an appropriate statistical model for a given dataset and conduct sensible statistical inference; |
| 4. | formulate a linear regression model and carry out appropriate statistical inference. Understand the limitations of the linear regression model and the implications of model misspecification; |
| 5. | analyse real-world datasets using modern statistical software. Apply theoretical knowledge from the lectures and tutorials to solve real-world problems; |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Apply: Develop theoretical and technical knowledge in an area of statistics, incorporating deductive reasoning to solve complex problems. (1.1)
- Analyse: Examine the principles and concepts of a range of fundamental areas in the mathematical sciences (calculus, discrete mathematics, linear algebra, probability, statistics and quantitative management). (1.2)
- Apply: Develop research skills and ability to solve outstanding problems, with a critical evaluation and analysis of the obtained results. (2.1)
- Analyse: Make arguments based on proof and conduct simulations based on selection of approaches (e.g. analytic vs numerical/experimental, different statistical tests, different heuristic algorithms) and various sources of data and knowledge. (2.2)
- Apply: Ability to work effectively and responsibly in an individual or team context. (3.1)
- Apply: Demonstrate self-reflection, and individual and independent learning strategies to extend existing knowledge. (4.1)
- Analyse: Develop information retrieval and consolidation skills to critically evaluate mathematical/statistical aspects of information to think creatively and try different approaches to solving problems. (4.2)
- Apply: Succinct and accurate presentation of information, reasoning and conclusions in a variety of modes, to diverse audiences (expert and non-expert). (5.1)
Contribution to the development of graduate attributes
This subject teaches students basic concepts in probability theory and their application in statistical modelling and inference. Students learn how to formulate an appropriate statistical model for a given dataset and how to carry out sensible statistical inference. The subject also trains the students in using modern statistical software to solve real-world problems and how to effectively communicate these solutions. Thus this subject is contributing to the following graduate attributes:
Graduate Attribute 1 - Disciplinary knowledge.
The lectures develop the theoretical understanding of the material. The tutorials allow the students to apply the theory to solve exercises and deepen their understanding of the material.
Graduate Attribute 2 - Research, inquiry and critical thinking.
The lectures present approaches to formulate statistical models of various types of data. The students will develop skills in determining the correct approach themselves in the tutorial classes.
Graduate Attribute 3 - Professional, ethical and social responsibility.
The tutorial classes encourage the students to work in groups under the supervision of a tutor. The computer lab is done in small groups and trains the students' ability to work effectively and responsibly.
Graduate Attribute 4 - Reflection, innovation, creativity.
The lectures teach the students to develop a creative mindset to solve a statistical problem. The tutorials give the students the opportunity to train their ability to design creative solutions to statistical problems. The computer labs train the students ability to critically evaluate statistical procedures and interpretation of results.
Graduate Attribute 5 - Communication.
Presentation of solutions to problems using appropriate professional language is emphasised in the computer labs.
Teaching and learning strategies
The subject consist of a combination of complementary in-class and self-study activities. Before class meetings, students are expected to engage with background material that will introduce the fundamental concepts covered in the subject. The face-to-face classes (two lectures (90 minutes and 60 minutes) per week, one 120 minutes weekly tutorial, and two 180 minutes computer labs) will incorporate a range of teaching and learning strategies, including individual and collaborative group work, presentation of worked examples and applying modern statistical software to analyse real-world datasets. Students are to review the relevant material made available on UTSOnline prior to classes.
Content (topics)
The major topics covered in this subject are:
- Basic concepts in probability theory
- Statistical inference and its connection to probability theory
- Critical thinking about data-based claims
Assessment
Assessment task 1: Online Exercises
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge 2. research, inquiry and critical thinking 4. reflection, innovation and creativity |
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| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 3 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 1.2, 2.1, 2.2 and 4.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 30% |
| Criteria: | Students will be assessed on:
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Assessment task 2: Computer lab exercises
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge 2. research, inquiry and critical thinking 3. professional, ethical and social responsibility 4. reflection, innovation and creativity 5. communication |
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| Objective(s): | This assessment task addresses subject learning objective(s): 1, 3, 4 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 1.2, 2.1, 2.2, 3.1, 4.1, 4.2 and 5.1 |
| Type: | Exercises |
| Groupwork: | Group, group assessed |
| Weight: | 20% |
| Criteria: | Students will be assessed on:
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Assessment task 3: Examination
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge 2. research, inquiry and critical thinking 4. reflection, innovation, creativity |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 1.2, 2.1, 2.2, 4.1 and 4.2 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 50% |
| Criteria: | Students will be assessed on:
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Minimum requirements
Student must obtain at least 40% of the marks available for the final examination in order to pass this subject. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50.
Students should demonstrate competence in all aspects of the assessment in order to pass the subject. To pass the subject, a student must achieve a final result of 50% or more. The final result is simply the sum of all the marks gained in each piece of assessment.
Recommended texts
Probability & Statistics for Engineers & Scientists - 9th Edition (Global Edition) by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye. Pearson 2016. Note that the book is the Global Edition.
The eBook version of the textbook can be obtained via the UTS library. It can also be purchased as an eBook direct from Pearson for $AUD 60.00. See links in UTSOnline under Subject Orientation. Alternative suppliers will also have this text.
NOTE: The tutorials rely on having access to the Global Edition of the textbook above, as the exercises to be solved are taken from the textbook. Students are strongly recommended to have a copy, either hard or electronic, with them to each tutorial session.