Mathematics 215: Introduction to Statistics

Course Orientation

Introduction

Welcome to Mathematics 215: Introduction to Statistics, a three-credit, university-level course designed to introduce and apply the basic principles of statistical analysis, including organization and presentation of statistical data, probability theory, probability distributions, estimation of population parameters from sample data, hypothesis-testing and bivariate analysis.

The ever-increasing availability of computers, statistical software packages, the Internet, internal and external electronic databases and computerized point-of-sales terminals has made the study of statistics an essential part of almost every discipline and profession. As a result, statistics practitioners are needed in diverse fields of study, such as chemistry, biology, medicine, nursing, sociology, criminology, psychology, geology, political science, economics, management and administration, finance, accounting and marketing.

When you have completed MATH 215, you will have acquired sufficient knowledge and skills to use statistics in making practical decisions and preparing reports in the workplace. As well, you will be in a much better position to complete papers and research projects in other university or college courses competently.

This Course Orientation contains information that you will need to complete MATH 215 successfully. Please read it carefully before you begin this course.

Learning Outcomes

After completing this course, you should be able to

• organize, summarize, and display data in a meaningful way.
• compute various measures of centre, variability and position of data sets.
• apply basic rules of probability to calculate likelihoods of random events.
• use appropriate probability distributions to estimate and test hypotheses about parameters of single and multiple populations.
• perform goodness-of-fit tests and analyse cross-tabulated data.
• use linear correlation and regression methods to analyse relationships in bivariate data.

Course Home Page

Before you begin, familiarize yourself with the MATH 215 course home page in Moodle.

Your course home page contains links to all the essential and supplementary resources for MATH 215. There you will also find your assignments and course discussion forums, and Assignment Drop Boxes where you can submit your assignments directly to your tutor. Questions can be directed to your tutor or the Computing Services Help Desk, as appropriate.

The Moodle Orientation for Students linked on the course home page will help you learn how best to use this online learning environment.

Course Materials

The course is taught using online resources and academic support.

eText

As a student registered in this course, you will have access to the digital textbook for the course:

Introductory Statistics, 9th ed., by Prem S. Mann (Hoboken, NJ: Wiley, 2016)

There are two ways to access this textbook: in its downloadable form through VitalSource (called the eText), and in its interactive form through WileyPLUS. In both versions of the textbook, you can print selected sections of the content.

Downloadable eText

Access the downloadable eText through VitalSource by using the eText link on the course home page. You can download it on up to five devices to use it for offline study. You may also print selected sections of the content. This is a permanent download, so you can keep it for future courses and throughout your career. This eText is organized by chapters and includes page numbers.

Interactive Textbook

Access the online, interactive version of your eText by using the WileyPLUS Course Resources link on the course home page. The content is organized by chapter and by study objective,providing a glossary of terms and exercises with solutions. Learn how to access WileyPLUS Course Resources.

To read from the textbook, select the chapter and section you are working on. Once you are in the reading pane, you can use the navigation column on the left side of the page to select different sections from the current chapter, as well as additional content and resources related to the chapter.

In most sections, at the top of the reading pane there will be a link to a video tutorial. There will also be a Videos link in the navigation column.

Optional WileyPLUS Assignments

The interactive version of the textbook in WileyPLUS includes additional exercises and assignments that you can complete if you want more practice with a particular topic. The assignments on WileyPLUS are for practice only. They are not required for the course. The only assignments that need to be submitted for marking are in the Evaluation section of the course home page.

Solutions to Exercise Questions

Your textbook contains answers and worked-out solutions to odd-numbered exercises.

To access these solutions from the interactive version of the textbook, click on WileyPLUS Course Resources. Select the chapter you are working on, and then select Student Solutions Manual in the navigation column on the left side of the page. Alternatively, you can expand the answers and solutions to odd-numbered questions from within the exercise questions themselves.

To access the solutions in the downloadable eText, select the section near the end of the eText titled “Answers to Selected Odd-Numbered Exercises and Self-Review Tests.”

Key Formulas

A Key Formulas document is provided for your reference on the course home page. These formulas are adapted from the textbook. The first two pages of formulas relate to Chapters 1–6 of the textbook (corresponding to Units 1–3 of the course), which are covered on the midterm exam, and the last two pages of formulas relate to Chapters 7–13 of the textbook (corresponding to Units 4–6 of the course), which are covered on the final exam.

You might want to use this sheet while you are working on solving exercises. You also might want to use it to help you create a summary sheet of notes and formulas to bring into your exams (this sheet can be no larger than 8.5 × 11 inches, double-sided). See the Summary Sheets section below for more information.

Athabasca University Materials

MATH 215: Introduction to Statistics—Course Orientation. Athabasca, AB: Athabasca University, 2020.

This Course Orientation provides essential information on the course materials, suggested study schedule and evaluations for the course, and the procedures you should follow to complete the course successfully. Please read it through carefully before beginning your studies.

MATH 215: Introduction to Statistics—Study Guide. Athabasca, AB: Athabasca University, 2020.

The Study Guide provides the structure for the course. Each unit of the Study Guide includes an introduction to the unit topic. Each section within a unit indicates its learning outcomes, and explains which readings, activities, exercises and assignments are required or recommended for the topics covered in that section. The Study Guide also contains unit self-tests that you should complete to measure your own comprehension.

Forms

The forms you will need to apply to write examinations and request extensions, as well as other forms you might need, are available through your myAU Portal.

Calculators and Other Technology

For the assignments and examinations, programmable calculators (e.g., TI-84, TI-83) are not permitted. The only calculator that you are allowed to bring into the exam room is the Texas Instruments TI-30Xa Scientific Calculator. It is inexpensive (approximately CA$14) and available from retailers such as Staples, Amazon, and Walmart. It is capable of calculating roots and exponents, but it is not programmable and does not have a statistics mode. You should familiarize yourself with its functionality from the beginning of the course so that you can complete the calculations as will be required on the assignments and exams. The memory of the calculator must be cleared before the examination.

Other electronic devices, such as laptop computers, desktop computers, personal desktop assistants, digital cameras, iPads, iPods, cell phones, smart watches, and any other personal communication devices are not permitted in the examination room except with pre-approval from the course professor.

As you work through the course, you may use a calculator with a statistics mode, but only for practice and to verify your work. You may also use programs such as Microsoft Excel and Minitab for practice and verification purposes only.

You are required to show all your work on assignments through substitution of appropriate sums into statistical formulas. It is important to be able to solve all questions using the methods and procedures outlined in the course materials. On the course assignments to be submitted for credit, any question in which a disallowed electronic device or application has been used to generate an answer will receive a grade of 0 marks. For example, using a calculator to obtain the standard deviation of a data set, without showing all of the mathematical/statistical work associated with that calculation, will result in a grade of 0 marks.

On both the midterm and final exams, the only calculator allowed into the examination room is the Texas Instruments TI-30Xa Scientific Calculator. Because the online exams contain only short-answer and machine-marked questions, no interim calculations may be shown unless requested by the exam question, itself. However, longer procedural questions are divided into parts, and partial marks are allotted in this way. For numeric (number) answers, be sure to enter the answer in the format requested by the question. For decimal answers, keep all work to at least four to six decimal places; only round the answer to the required number of decimal places as the last step before inputting the final answer. You are not required to type mathematical symbols, formulas or equations, nor are you required to show tables and graphs, on the exams.

We are aware that some scientific calculators that are capable of computing square roots and exponents also include certain built-in statistics functions. Do not use these functions to generate answers on an exam.

Course Outline

MATH 215 is divided into six units, which cover descriptive and inferential statistics. Each unit is divided into several sections.

Unit 1: Descriptive Statistics is designed to teach you how to organize, summarize and display statistical data in a meaningful way. The content of this unit is divided into the following sections:

1-1Statistics and Basic Terms 1-2Types of Variables and the Nature of Statistical Data 1-3Population, Sampling, Design of Experiments, and Summation Notation 1-4Organizing and Graphing Qualitative Data 1-5Organizing and Graphing Quantitative Data 1-6Measures of Central Tendency for Ungrouped Data 1-7Measures of Dispersion for Ungrouped Data 1-8Mean, Variance and Standard Deviation for Grouped Data 1-9Using Standard Deviation 1-10Measures of Position and Box-and-Whisker Plots

Unit 2: Probability introduces basic probability theory, including the addition and multiplication rules of probability, joint probability and conditional probability. The content of this unit is divided into the following sections:

2-1Experiment, Outcomes and Sample Space 2-2Determining Probabilities: Three Conceptual Approaches 2-3Marginal and Conditional Probabilities 2-4Intersection of Events and the Multiplication Rule 2-5Union of Events and the Addition Rule 2-6Counting Rules, Factorials, and Combinations

Unit 3: Probability Distributions explores the concept of probability distribution, including mean and variance, and applies this concept to two commonly used probability distributions in statistics: the binomial distribution and the normal distribution. The content of this unit is divided into the following sections:

3-1Random Variables and Probability Distribution of a Discrete Random Variable 3-2Mean and Standard Deviation of a Discrete Random Variable 3-3The Binomial Probability Distribution 3-4The Standard Normal Distribution 3-5The Normal Distribution 3-6The Normal Approximation to the Binomial Distribution

Unit 4: Estimation and Tests of Hypotheses for One Population introduces the concepts of sampling distribution and the central limit theorem, and shows how these two important concepts are used to estimate population parameters and test hypotheses from samples randomly selected from one population. The content of this unit is divided into the following sections:

4-1Mean and Standard Deviation of the Sampling Distribution of the Sample Mean 4-2Shape of the Sampling Distribution of the Sample Mean 4-3Mean, Standard Deviation, and Shape of the Sampling Distribution of the Sample Proportion 4-4Estimation of a Population Mean: Population Standard Deviation Is Known 4-5Estimation of a Population Mean: Population Standard Deviation Is Unknown 4-6Estimation of a Population Proportion: Large Samples 4-7Hypotheses Tests about the Population Mean: Population Standard Deviation Is Known 4-8Hypotheses Tests about the Population Mean: Population Standard Deviation Is Unknown 4-9Hypotheses Tests about the Population Proportion: Large Samples

Unit 5: Tests of Hypotheses for Two or More Populations extends your study of statistical inference to completing hypothesis tests involving the mean and proportion for two or more populations. As well, you will examine other common tests of hypotheses, including comparison of means for more than two populations, goodness-of-fit tests, analysis of cross-tabulated data, and tests of variance and standard deviation. The content of this unit is divided into the following sections:

5-1Inferences about the Difference between Two Population Means for Independent Samples: $\sigma 1$ and $\sigma 2$ Known 5-2Inferences about the Difference between Two Population Means for Independent Samples: $\sigma 1$ and $\sigma 2$ Unknown but Equal 5-3Inferences about the Difference Between Two Population Means for Paired Samples 5-4Inferences about the Difference Between Two Population Proportions for Large and Independent Samples 5-5Goodness-of-Fit Tests 5-6Tests for Independence and Homogeneity 5-7Inferences about the Population Variance 5-8Analysis of Variance

Unit 6: Bivariate Analysis focuses on the relationship between two variables, using correlation analysis to determine the strength of the relationship, and regression analysis to establish a mathematical formula for the relationship. The content of this unit is divided into the following sections:

6-1Simple Linear Regression Analysis 6-2Standard Deviation of Random Errors and the Coefficient of Determination 6-3Inferences about $B$ 6-4Linear Correlation 6-5Applying Correlation and Regression

Study Guide

You will find each of these units detailed in the Study Guide. The Study Guide points you to the required readings and exercises in the textbook for each section of each unit. Your textbook provides detailed solutions for the required exercises. Each unit closes with a self-test that enables you to evaluate your mastery of the material. The link to the solutions to the unit self tests are located on the course home page in the Study Guide section.

After you complete the self-test for a given unit, complete the unit assignment and submit it to your tutor for grading. The assignments are available on the course home page in the Assessments section.

Once you have successfully completed the first three units of this course, you will be ready to take the midterm examination. Once you have successfully completed the last three units of this course, you will be prepared to write the final examination.

Study Schedule

MATH 215 is a three-credit (one-semester) course designed to be completed in about 24 weeks. Students registered in the individualized-study version of the course are permitted to take up to six months, but we recommend following a 24 week schedule; it will leave you with extra time that will be helpful if there are unexpected delays or emergencies. See the study schedule link at the right side of the course home page to create a customized schedule for yourself.

If you find yourself falling behind, contact your tutor to discuss the situation. You may also extend your course contract; however, there is a fee for this and there are important deadlines as to the latest time in your course contract that you may apply for such extensions. Also note that examinations must be written within your six-month contract period (unless you have obtained an extension) and that there are deadlines concerning how soon you must apply to write an examination prior to the date on which you wish to write the examination. These deadlines can be quite early, depending on your circumstances. Extension deadlines and examination request deadlines are explained in the undergraduate Calendar and the Student Manual. Check them carefully before your contract end date.

24-Week Suggested Study Schedule

Study Schedule for download

Student Evaluation

Your final grade in MATH 215 is based on the grades you achieve in six unit assignments, a midterm examination and a final examination.

To pass this course, you must achieve a mark of at least 50% on each of the following: (a) the midterm examination, (b) the final examination and (c) the composite course grade which includes both exam and the assignment grades.

The following chart indicates the assessments for this course, their weighting toward your final grade, the units covered by each one, and the time that each one is due.

Assignments

The assignments to be submitted for credit may be found under the Assessment section on the home page. There are six (6) assignments for credit, one for each unit of the course. They are designed to challenge you. They will contain only problems that you can solve using the skills and knowledge you acquired while working through the course, but you may need to combine that knowledge and those skills in unexpected ways. Download the assignments from the Assessments section of the course home page.

Unit Self-Tests

At the end of each unit of the Study Guide, there is a unit self-test provided for practice and self-assessment purposes. The questions on these unit self-tests are in a format similar to the format of the questions on the exams. However, the exam questions are configured in a short-answer, machine-marked format. You are not required to type mathematical symbols, formulas or equations, nor are you required to show tables and graphs, on the exams. The solutions documents for the unit self-tests are linked on the course home page. It is advisable to try to complete these self-tests without resorting to the textbook or the solutions document.

Extra Practice for Self-Assessment

At the end of each chapter of the textbook, there is a list of optional extra practice questions. Solutions to these questions are accessible in either the Answers to Selected Odd-Numbered Exercises section of the downloadable eText or in the Student Solutions Manual in the interactive textbook.

WileyPLUS Optional Practice Questions

You can complete these practice questions as a review, particularly before beginning an assignment or before an exam. They are particularly useful in helping you to determine quickly the type of question being asked. However, it is not advisable to utilize these as your sole practice in this course because the questions are not in the same format as the questions on the assignments or exams for the course.

Technology

At the end of each chapter in the eText, there are TI-84, Excel and Minitab instructions for chapter-specific statistical calculations or processes. Knowledge of these statistical software packages is not required for MATH 215. Students who already have access to any of these applications may choose to use them to double check their work. However, these applications cannot be accessed for use on either of the midterm and final exams. Only the TI-30Xa Scientific Calculator may be brought into an exam room so it is advised to become accustomed with its functionality in order to do the calculations required on an assignment or during an exam.

Examinations

The midterm examination is worth 40% of your final grade and will cover material presented in Units 1–3 of the course (which cover material from Chapters 1–6 of the textbook). The final examination is also worth 40% of your final grade and will cover material presented in Units 4–6 of the course (which cover material from Chapters 7–13 of the textbook). Both the midterm and final are closed-book, short-answer and machine-marked exams in the Möbius online platform and are invigilated through ProctorU. You will have three (3) hours to complete each exam and will not be permitted to take any breaks or leave the examination room. See Requesting, Accessing and Navigating Your Möbius Exam for more information.

Examination Format

Both the midterm and final are closed-book, short-answer and machine-marked exams in the Möbius online platform and are invigilated through ProctorU. You will have three (3) hours to complete each exam and will not be permitted to take any breaks or leave the examination room. See Requesting, Accessing and Navigating Your Möbius Exam for details.

The examinations consist of problems similar in nature to those presented in the unit self-tests and the unit assignments, but are configured for a short-answer, machine-marked, online format.

For numeric (number) answers, be sure to enter the answer in the format requested by the question. For decimal answers, keep all work to at least four to six decimal places; only round the answer to the required number of decimal places as the last step before inputting the final answer. You are not required to type mathematical symbols, formulas or equations, nor are you required to show tables and graphs.

Summary Sheets

Formula sheets will not be provided with the examinations; however, probability distribution tables needed to solve exam questions will be accessible at the top of the Möbius exam question pages.

You are allowed to bring to each exam one double-sided, 8.5 × 11-inch summary sheet (not an 8.5 × 14-inch legal sheet) that may include formulas, graphs and personal notes. For this, you may use a portion of the Key Formulas document linked on the course home page, or you may create your own formula sheet. The summary sheet must not contain additional attachments, such as sticky notes, stapled pages, etc. You may also bring scrap paper to each exam.

Your summary sheet and scrap paper must be torn up/destroyed in front of the ProctorU invigilator at the end of each exam. Therefore, you will need to create a separate summary sheet for each exam.

Allowable Calculators

See the Calculators and Other Technology section of this Course Orientation for information on allowable calculators and policies on other technology.

Evaluation Criteria for Assignments and Online Exams

Students are required to show all work on assignments to be submitted for credit through substitution of appropriate values into statistical formulas using the methods and procedures outlined in the course materials. Partial marks will be awarded.

For the course assignments, show all of your calculations, explanations and reasoning, and always answer the original question(s). Finishing a test of hypotheses with a statement like “reject Ho” or “do not reject Ho” is insufficient for full marks; you must also provide a written concluding statement in the context of the problem, itself. In addition, any question in which a disallowed electronic device or application has been used to generate an answer will receive a grade of 0 marks. For example, using a scientific calculator that has some statistics functions or an application to obtain the standard deviation of a data set, without showing all of the mathematical/statistical work associated with that calculation, will result in a grade of 0 marks.

Because the online exams contain only short-answer and machine-marked questions, no interim calculations may be shown, unless requested by the exam question, itself. However, longer procedural questions are divided into parts, and partial marks are allotted in this way.

For numeric (number) answers, be sure to enter the answer in the format requested by the question. For decimal answers, keep all preliminary work to at least four to six decimal places; only round the answer to the required number of decimal places as the last step before inputting the final answer. You are not required to type mathematical symbols, formulas or equations, nor are you required to show tables and graphs, on the exams.

Exam Requests

All exams in this course are written in the online Möbius platform. Be sure to request each exam well in advance of the date you intend to write it. Take the time to review the process for Requesting, Accessing and Navigating Your Möbius Exam.

Do not click an exam link unless you have both (a) booked your exam with ProctorU; and (b) requested your exam through the Office of the Registrar.

Supplementary Exams

Requesting Transcripts

https://www.athabascau.ca/registrar/oros-help/transcript-request.html

For further information, please see the section of the Student Manual titled “Applying for and Writing Examinations.”