Mathematics 216 Computer-oriented Approach to Statistics

Course Orientation

Introduction

Welcome to MATH 216, a three-credit junior-level course designed to introduce and apply the basic principles of statistical analysis, including organization and presentation of statistical data, probability theory and probability distributions, estimation of population parameters from sample data, hypothesis testing, and bivariate analysis.

An important feature of MATH 216 is its computer component. After you have completed the exercises from the textbook, you will review and apply the statistical theory using statistical software, the eText, and online computer labs. These materials will teach you how to use an industry standard statistical software application called StatCrunch to solve statistics problems.

When you have completed MATH 216, you will have acquired sufficient knowledge and computer related 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 competently complete papers and research projects in other university or college courses.

We cannot overestimate the value of a course that encourages you to use computer software to apply the tools of statistics in today’s society, which is increasingly dependent on electronic sources of information such as intranets, private and public online databases, the Internet, electronic instruments, and point-of-sale electronic terminals.

There are no prerequisites for MATH 216; however, students are expected to have certain skills in mathematics, including basic knowledge of high school algebra. If you have doubts about your ability to handle the mathematics involved in this course, contact the course coordinator to discuss your situation.

This Course Orientation contains information that you will need to successfully complete MATH 216. Please read it carefully before you begin this course, and refer to it as you progress through the Study Guide units.

Learning Outcomes

Upon successful completion of this course, you should be able to

  • apply the basic principles of statistical analysis using statistical software.
  • employ the tools of descriptive statistics to organize, summarize and present information in a meaningful way.
  • predict the likelihood of real world events, based on rules of probability and common probability distributions.
  • estimate and test hypotheses regarding characteristics of both single and multiple populations.
  • identify patterns of relationships between qualitative variables.
  • employ linear correlation and regression methods to analyze relationships between quantitative variables.
  • responsibly use statistical methods by testing the underlying assumptions.

When you have successfully completed MATH 216, you will have acquired sufficient knowledge and computer related skills to utilize statistics in making practical decisions and preparing reports in the workplace. As well, you will be in a much better position to competently complete papers and research projects in other university or college courses.

Course Materials

MATH 216 is taught using online resources created by Athabasca University, digital web-based materials from the textbook publisher, and academic support from your tutor.

eText

The following textbook is available as an eText and is accessible on the course home page:

Larson, R., & Farber, B. (2019). Elementary statistics: Picturing the world (7th ed.). New York: Pearson.

Learn about the features of your eText and how to download it for offline use, so that you can keep it after you have completed this course; print pages; search; cite passages; and manage notes and highlights. Learn about privacy issues and where to go for help.

All the resources below are accessible from your course home page.

Online resources published by Athabasca University

Math 216: Computer-oriented Approach to Statistics. Course Orientation. Athabasca, AB: Athabasca University, 2020.

Math 216: Computer-oriented Approach to Statistics. Study Guide. Athabasca, AB: Athabasca University, 2020.

Math 216: Computer Labs (Technology Manual). Athabasca, AB: Athabasca University, 2020.

Online resources on the Pearson MyLab website

Pearson MyLab

  • Student’s Solutions Manual. In the MyLab Statistics menu on the left, click Chapter Contents > Student’s Solutions Manual.
  • StatCrunch statistical software (also available at statcrunch.com)
  • Pearson MyLab Study Plan (Optional)
  • Multimedia Resources (Optional)

For help accessing this resource, see Accessing Pearson MyLab on the course home page.

Note: Students enrolled in MATH 216 must have a scientific calculator, which is a calculator that can perform exponential operations. You may wish to use a scientific calculator that has a statistics mode to save computation time. However, you will be required to show all work on assignments and exams through substitution of appropriate values into statistical formulas. When using the calculator for computation, please do not round off any of your middle work. Round your final answers to four decimal places. Programmable calculators such as the TI-84 Plus are not permitted on exams.

About the Study Guide

The Study Guide is your detailed map for progressing through all the topics and activities that make up this course. Follow it closely to ensure that you do not miss key activities in this course.

The Study Guide is organized into six units, each of which is broken down into several topics that:

  • Provide you with the learning objectives that you are responsible for in each section of your textbook.
  • Direct you to important reading and practice exercises in your textbook.
  • Direct you to solutions to practice exercises.
  • Direct you to important computer problems as well as step-by-step guides to solving these problems using statistical software.

Each unit in the Study Guide closes with a unit self-test that allows you to judge your mastery of the material in that unit. The six unit self-tests help you prepare for the six assignments you will submit for evaluation and credit.

As you progress through the Study Guide, get into the habit of showing all the work you do on the assigned exercises in a notebook. Remember, on your assignments and examinations, you must always show exactly how you arrived at your answer; if your answer is incorrect, your tutor will be able to tell you exactly where you went wrong.

Course Structure

MATH 216 is divided into six units, covering descriptive and inferential statistics.

Unit 1. Descriptive Statistics

Designed to teach you how to organize and present statistical data in a meaningful way.

Unit 2. Probability

Introduces basic probability theory, including the addition and multiplication rules of probability, joint probability, and conditional probability.

Unit 3. Probability Distributions

Discusses probability distributions commonly used in statistics: binomial and normal probability distributions.

Unit 4. Inference on One Sample

Introduces the concepts of sampling distribution and the central limit theorem, and shows how these two important concepts are used to estimate population parameters from sample statistics. In the section on hypothesis testing, you will see how a claim regarding a characteristic of one population is made and how sample data is used to test the claim.

Unit 5. Inference on Two Samples

Presents techniques for comparing two populations using confidence intervals and tests of hypotheses.

Unit 6. Bivariate Analysis

Focuses on relationships between two variables. Correlation analysis is used to determine the strength of the relationship between two quantitative variables. Regression analysis is used to establish a mathematical formula for the relationship between two quantitative variables. The test of independence topic examines the relationship between two categorical (qualitative) variables. Analysis of variance is a technique to compare the means of three or more populations. Analysis of variance can provide valuable information on the relationship between a qualitative and quantitative variable.

Note: We strongly recommend that you follow the weekly schedule in this Course Orientation. Remember that you must complete all of the assignments before you write the final examination.

Weekly Schedule

The suggested weekly schedule below indicates the approximate amount of time you should spend on each course topic and activity. Topics to study and activities to complete are given in the Study Guide.

Although you have six months from your start date to complete the course, you will note that the schedule is based on a 22-week period. This time frame is closely in line with schedules of similar courses in traditional institutions, and allows you some leeway should an unforeseen event interrupt your studies.

Take the time now to think about your own target calendar dates for each week. If you find yourself falling behind, contact your tutor to discuss the situation. The course is challenging, but you should have no difficulty meeting these guidelines if you set aside consistent study periods each week and do not procrastinate.

We highly recommend that you follow the Weekly Schedule provided below.

Download a PDF of the weekly schedule.

Week

Activity

Week 1

Read this Course Orientation and the Student Manual.

Contact your tutor.

Begin reading the Study Guide:

○  Introduction to Unit 1
○  Overview of Statistics
○  Data Classification
○  Data Collection and Experimental Design
○  Computer Lab 1A

Week 2

○  Frequency Distributions and Their Graphs
○  More Graphs and Displays
○  Measures of Central Tendency

Week 3

○  Measures of Variation
○  Measures of Position
○  Computer Lab 1B

Week 4

○  Self-Test 1 (Theory and Computer Components)
○  Assignment 1 (Theory and Computer Components)

Submit Assignment 1 using the online drop box on the course home page.

Week 5

○  Introduction to Unit 2
○  Basic Concepts of Probability and Counting
○  Conditional Probability and the Multiplication Rule

Week 6

○  The Addition Rule
○  Additional Topics in Probability and Counting
○  Computer Lab 2

Week 7

Apply for the midterm exam.

○  Self-Test 2 (Theory and Computer Components)
○  Assignment 2 (Theory and Computer Components)

Submit Assignment 2 using the online drop box on the course home page.

Week 8

○  Introduction to Unit 3
○  Probability Distributions
○  Binomial Distributions
○  Computer Lab 3A
○  Introduction to Normal Distributions and the Standard Normal Distribution.

Week 9

○  Normal Distributions: Finding Probabilities
○  Normal Distributions: Finding Values
○  Computer Lab 3B

Week 10

○  Self-Test 3 (Theory and Computer Components)
○  Assignment 3 (Theory and Computer Components)

Submit Assignment 3 using the online drop box on the course home page.

Week 11

Study for midterm exam.

Take midterm exam.

Week 12

○  Introduction to Unit 4
○  Sampling Distributions and the Central Limit Theorem
○  Confidence Interval for the Mean (σ Known)
○  Confidence Intervals for the Mean (σ Unknown)

Week 13

○  Confidence Intervals for Population Proportions
○  Computer Lab 4A
○  Introduction to Hypothesis Testing with One Sample
○  Hypothesis Testing for the Mean (σ Known)
○  Hypothesis Testing for the Mean (σ Unknown)

Week 14

○  Hypothesis Testing for Proportions
○  Computer Lab 4B

Week 15

○  Self-Test 4 (Theory and Computer Components)
○  Assignment 4 (Theory and Computer Components)

Submit Assignment 4 using the online drop box on the course home page.

Week 16

○  Introduction to Unit 5
○  Testing the Difference Between Means (σ1 and σ2 Known)
○  Testing the Difference Between Means (σ1and σ2 Unknown)

Week 17

○  Testing the Difference Between Means (Dependent Samples)
○  Testing the Difference Between Proportions
○  Computer Lab 5

Week 18

Apply for the final exam.

○  Self-Test 5 (Theory and Computer Components)
○  Assignment 5 (Theory and Computer Components)

Submit Assignment 5 using the online drop box on the course home page.

Week 19

○  Introduction to Unit 6
○  Correlation
○  Linear Regression
○  Measures of Regression and Prediction Intervals
○  Computer Lab 6A

Week 20

○  Test of Independence
○  Analysis of Variance (ANOVA)

Week 21

○  Computer Lab 6B
○  Self-Test 6 (Theory and Computer Components)
○  Assignment 6 (Theory and Computer Components)

Submit Assignment 6 using the online drop box on the course home page.

Week 22

Study for final exam.

Take final exam.

Student Evaluation

Your final grade in MATH 216 is based on the grades you achieve in six assignments, a midterm examination, and a final examination.

Each assignment is worth 5% of your final grade. When you submit each assignment for marking, be sure to send both the theory and the computer components at the same time, using the corresponding online drop box on the course home page. For each assignment, the theory component is worth 80% and the computer component 20%.

Note: The assignments are designed to challenge you. They 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 the knowledge and skills in unexpected ways.

The midterm examination is worth 35% of your final course grade. It will consist of a theory component worth 28% of your final course grade and a computer component worth 7% of your final course grade. The midterm examination will be a supervised exam conducted in a manner consistent with the examination policy described in the Athabasca University calendar. The midterm examination will test you on the course material covered in Units 1 to 3 of the course.

The final examination is worth 35% of your final course grade. It will consist of a theory component worth 28% of your final course grade and a computer component worth 7% of your final course grade. The final examination will be a supervised exam conducted in a manner consistent with the examination policy described in the Athabasca University calendar. The final examination will test you on the course material covered in Units 4 to 6 of the course.

In total, the theory section of the course makes up 80% of your composite course grade and the computer-related questions and assignments contribute 20% to your composite grade.

To pass this course, you must achieve a mark of at least 50% on each of the following:

  • the theory component of the midterm examination
  • the computer component of the midterm examination
  • the theory component of the final examination
  • the computer component of the final examination.

Your composite course grade must also be at least 50% for you to pass this course.

Note: Students who do not achieve a minimum passing grade of 50% on any examination theory or computer component will be allowed to write one supplemental for each examination component.

Examination Procedures and Materials

!

Important

All exams in this course will be written in the 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 on the course home page unless you have both (a) booked your exam with ProctorU and (b) requested your exam through the Office of the Registrar. Note that ProctorU is the only invigilator available for the MATH 216 Möbius exams.

The midterm examination will cover Units 1 to 3. The final examination will cover Units 4 to 6.

Note: In both the midterm and the final examination, you are allowed to bring in one 8½ × 11 inch summary sheet that can include anything you feel may help you complete the exam successfully. The summary sheet may contain formulas and worked-out examples. You may use both sides of this summary sheet.

No books or notes may be used during the exam other than the double-sided summary sheet noted above. For security reasons, your invigilator will ask you to destroy your summary sheet at the end of your exam. Therefore, you may wish to make a copy in case you are required to or decide to write a supplemental examination.

You are expected to use a standard scientific calculator in each exam. You may not use programmable calculators, graphing calculators (such as the TI 83 or TI 84 Plus etc.), computers, and other mobile devices during the exam.

To study for each exam, we suggest the practices below. (We will use the midterm as an example.)

  1. For each topic in Units 1 to 3 of the Study Guide, review each Learning Objective along with the work you have shown when completing each exercise you were assigned in the related section.
  2. Redo the self-tests for Units 1 to 3.
  3. Redo the assignments for Units 1 to 3.

Follow the same approach when studying for the final exam.

Getting Off to the Right Start

We suggest the following steps when working through this course.

  1. Read through this entire Course Orientation and briefly review the course materials.
  2. Before you begin any unit of the Study Guide, check the Weekly Schedule in the Course Orientation. Be sure you have identified weekly dates so that you can pace yourself appropriately through this course.
  3. In the Study Guide, scan the Contents column of Unit 1, and read the Introduction to Unit 1.
  4. Proceed to the Unit 1 topic “Overview of Statistics.”
    • Review key learning objectives related to this topic.
    • Read the specified pages in your textbook.
    • Work through the Try It Yourself exercises related to Unit 1.

    • Work through the suggested exercises in the textbook in Unit 1.

      Note: The most important activity in this course is the completion of the suggested exercises in the Study Guide units. We encourage you to show your work when completing each exercise and keep all your work in a notebook. This practice will help you prepare for your assignments and exams.

  5. The Study Guide will direct you to complete a few more topics in Unit 1.
  6. Next is Computer Lab 1A, several activities to complete using the statistical software StatCrunch.
  7. After you complete the remaining topics in Unit 1, work through Self-test 1. Again, be sure to show all your work when completing the self‑test.
  8. Complete the assignment and submit it using the drop box on the course home page. Be sure to keep a backup copy of the submitted assignment.
  9. Follow Steps 2 to 8 above for each unit of this course.

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