math 216 assignment 5

Mathematics (MATH) 216

Delivery mode:

Individualized study online with eText

Area of study:

Prerequisites:

None. Fundamental mathematical skills are required, particularly the ability to do basic algebra. Reviews of basic mathematics are available at Athabasca University Library. MATH 101  (a non-credit course) is suitable preparation for taking MATH 216, for those students concerned about their mathematical background. Familiarity with the Windows operating system is essential.

Course start date:

If you are a:

• Self-funded student: register by the 10th of the month, start on the 1st of the next.
• Funded student: please check the next enrolment deadline and course start date .

MGSC 301 , MATH 215 . (MATH 216 may not be taken for credit if credit has already been obtained for MGSC 301 or MATH 215.)

MATH 216 is not available for challenge.

Faculty of Science and Technology

Both the midterm and final are closed-book, machine-marked exams in the Möbius online platform and are invigilated through ProctorU . See the Evaluation section of the syllabus for more information.

Mathematics Diagnostic Assessment . This online test contains 70 questions that will help you assess your mathematical skills. Based on your score, we will recommend which Athabasca University mathematics course you are likely ready to take successfully.

The web-based statistical software used in MATH 216 is compatible with the following operating systems: Windows 10, 8.1. 8, and 7; Mac OS 10.12 – Sierra, 10.11 - El Capitan, 10.10 – Yosemite.

Learning outcomes

Important links.

MATH 216 gives students a working knowledge and understanding of descriptive and inferential statistics and how statistics is applied in the sciences, social sciences, and business. An important feature of MATH 216 is its computer component, which teaches you how to use an industry standard statistical software application to apply the tools of statistics to make practical decisions, prepare reports in the workplace, and effectively complete papers and research projects in other university courses. We cannot underestimate the value of a course which encourages you to use computer software to apply the methods of statistics, in a society which is increasingly dependent on electronic sources of information such as intranet databases, external databases, the internet, electronic instruments, and point of sales electronic terminals. MATH 216 is a multimedia course designed to appeal to a wide range of students with diverse learning styles.

• Unit 1: Descriptive Statistics
• Unit 2: Probability
• Unit 3: Probability Distributions
• Unit 4: Inference on One Sample
• Unit 5: Inference on Two Samples
• Unit 6: Bivariate Analysis

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.

To receive credit for MATH 216, you must achieve a mark of at least 50 percent on both the midterm and final examinations, and y our composite course grade must be at least  D (50 percent) .

The midterm and final are closed-book, machine-marked exams in the Möbius online platform and are invigilated through   ProctorU . Your exams must be requested in advance, and you must pay the ProctorU invigilation fees. You will have three (3) hours to complete each exam.

Note: You are expected to use a standard scientific calculator in each exam. Programmable calculators, graphing calculators (such as the TI83, etc.), computers, or any other mobile electronic devices may not used during the exams.

The weighting of the composite course grade is as follows:

To learn more about assignments and examinations, please refer to Athabasca University’s online Calendar .

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

Registration in this course includes an electronic textbook. For more information on electronic textbooks , please refer to our eText Initiative site .

Online Resources at Pearson MyLab Website

• Student's Solutions Manual
• StatCrunch statistical software (also available at statcrunch.com)
• MyLab Study Plan (Optional)
• Multimedia Resources (Optional)
• Academic advising
• Program planning
• Request assistance
• Support services

Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized study counterparts.

Opened in Revision 4, June 10, 2020

Updated January 16, 2024

View previous revision

• Course Orientation
• Study Guide
• Computer Lab Guided Solutions (Technology Manual)
• Computer Lab Quick Review
• Self-Test B (Computer Component) Solutions

The Course of Empire, Destruction, Thomas Cole, 1836 (Wikimedia Commons, public domain)

Mathematics 216 Computer-oriented Approach to Statistics

Study Guide :: Unit 3

• Probability Distributions

Introduction

In Unit 2, given a probability experiment, you assigned probabilities to various events based on probability concepts and rules. In Unit 3, you will use specific probability distributions to compute probabilities for various events.

You will begin by discussing probability distributions at a general level. A probability distribution describes a list of all possible outcomes for an experiment, along with the probabilities of each of these outcomes. Each outcome is described as specific values of a random variable . A random variable ( x ) represents a numerical value associated with each outcome of a probability experiment. After you construct a probability distribution, you can compute the mean or expected value, variance, and standard deviation of the probability distribution.

Once you understand the notion of a probability distribution in a general sense, you will examine  discrete probability distributions . These distributions involve discrete random variables . Discrete random variables can assume only certain distinct values, typically determined through a counting process. In this unit, you will study the discrete binomial probability distribution .

The most common probability distribution that statisticians deal with is a continuous probability distribution called the normal probability distribution . Such a distribution is also called a bell curve or a mound-shaped curve, terms that describe the shape of the graphical representation of the probability distribution: a smooth, bell-shaped curve that is symmetrical around the mean of the distribution.

The exact shape of the normal curve, and therefore the probability distribution, is determined by the mean and the standard deviation of the distribution. A normal distribution with a mean of zero and a standard deviation of one unit is called a standard normal probability distribution . Any normal distribution can be transformed into a standard normal distribution using a transformation formula that converts statistical observations into the standardized values of a standard normal distribution. This transformation will enable you to compute probabilities using the Standard Normal Distribution table of probabilities (Table 4, at the back of your textbook).

When you have completed this unit, you will be ready to study topics of inferential statistics, in which you will make statements about population parameters based on sample statistics.

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

• discrete probability distribution; standard deviation of a discrete probability distribution
• mean (expected value)
• random variables; discrete random variables; continuous random variables
• Given a probability experiment, construct a discrete probability distribution in table and graph format.
• Given a discrete probability distribution, compute the mean, variance, and standard deviation of this distribution.
• Compute the expected value of a discrete probability distribution. Interpret your results in terms of the context of the problem.

Important Note : For help accessing the e-text resources referred to below, see the navigation notes under eText on the course home page.

Required Reading

Elementary Statistics , Chapter 4, Section 4.1 Probability Distributions (pages 190-196)

Try It Yourself Examples

Work through each Try It Yourself example in this section of the e-textbook. Check your work against the solutions provided.

Exercises in Your e-Textbook

Do the following exercises in your e-textbook:

Chapter 4, Section 4.1 Exercises 5, 13, 15, 25, 27, 29, 31, 37 (pages 197-200). Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

• Binomial Distributions
• binomial experiment
• mean and standard deviation of a binomial distribution.
• Given a word problem, identify the problem as a binomial experiment.
• Compute binomial probabilities using binomial tables.
• Given a binomial probability distribution, compute the mean and standard deviation of this distribution.

Elementary Statistics , Chapter 4, Section 4.2 Binomial Distributions (pages 201-209)

Chapter 4, Section 4.2 Exercises 11, 13, 15, 19 (pages 210-211). Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 4 Section 4.2 are available on the textbook publisher’s MyStatLab website.

Chapter 4 Review ( Extra Online Practice )

For more practice working with the topics in this chapter of the e-textbook, work through this review. Or, if you feel you have mastered this material, you may skip to Computer Lab 3A.

Review Learning Objectives

Before proceeding to the online exercises, briefly review the Learning Objectives for each of the following topics, which are presented in previous sections of this study guide.

Optional Practice in Study Plan at MyStatLab

For more practice on the topics/sections of this chapter of your e-textbook, visit MyStatLab, and work interactively through the exercises in the Study Plan. For help accessing this resource, see MyStatLab navigation hints on the course home page.

Computer Lab 3A

Computer lab 3a detailed instructions.

In Computer Lab  3A, you will learn to use StatCrunch to develop solutions to exercises related to topics in Chapter 4 of your e-text.

For Computer Lab 3A activities, and step-by-step instructions (Guided Solutions) to familiarize you with StatCrunch, see the Computer Lab 3A file.

Computer Lab 3A Quick Reviews

The Quick Reviews (QRs) summarize a few key steps (but not all steps) needed to complete each Activity in Computer Lab 3A. These QRs will be useful when you are preparing for the computer components of the assignments, midterm exam, and final exam. To access, the QRs, click Computer Lab 3A QRs .

• Introduction to Normal Distributions
• continuous random variable
• normal distribution
• standard normal distribution
• Describe the key properties of a normal distribution.
• Describe the key properties of a standard normal distribution.
• Using standard normal distribution tables, find the numerical values for areas under the standard normal curve.
• Using standard normal distribution tables, find the probabilities associated with different z -score intervals. We strongly suggest that you first sketch the corresponding area under the standard normal curve, before using the standard normal distribution tables.

Elementary Statistics , Chapter 5, Section 5.1 Introduction to Normal Distributions and the Standard Normal Distribution

Chapter 5, Section 5.1 Exercises 17, 19, 21, 23, 27, 31. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 5 Section 5.1 are available on the textbook publisher’s MyStatLab website.

• Normal Distributions: Finding Probabilities

Learning Objective

After completing the readings and exercises assigned for this topic, you should be able to achieve the following learning objective.

• Using the standard normal distribution tables at the back of the textbook, find the probabilities associated with different x intervals for normal distributions with any mean and standard deviation. We strongly suggest that you first sketch the corresponding area under the normal curve before using the standard normal distribution tables.

Elementary Statistics , Chapter 5, Section 5.2

Chapter 5, Section 5.2 Exercises 13, 15, 17, 19. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 5 Section 5.2 are available on the textbook publisher’s MyStatLab website.

• Normal Distributions: Finding Values
• Using standard normal distribution tables (e.g., Appendix B, Table 4), find the z -scores associated with different areas under the normal curve.
• Using standard normal distribution tables (e.g., Appendix B in the e-text), find the z -scores associated with different percentiles.
• Find the x -value corresponding to a given z -score.
• Given a normal probability for a normal distribution with any mean and standard deviation, first sketch the given area (probability) under the normal curve, and then use standard normal distribution tables (e.g., Appendix B in the e-text) to find a specific data value ( x -value).

Elementary Statistics , Chapter 5, Section 5.3 Normal Distributions: Finding Values (pages 252-256)

Chapter 5, Section 5.3 Exercises 1, 3, 5, 9, 13, 17, 19, 21, 31, 39 (pages 257-259). Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 5 Section 5.3 are available on the textbook publisher’s MyStatLab website.

Chapter 5 Review ( Extra Online Practice )

For more practice working with the topics in Sections 1-3 of chapter 5 of the e‑textbook, work through this review. Or, if you feel you have mastered this material, you may skip Computer Lab 3B.

Computer Lab 3B

Computer lab 3b detailed instructions.

In Computer Lab  3B, you will learn to use StatCrunch to develop solutions to exercises related to topics in Chapter 5 of your e-text.

Your Computer Lab 3B activities, and step-by-step instructions (Guided Solutions) to familiarize you with StatCrunch, are in the Computer Lab 3B file on your course home page.

Computer Lab 3B Quick Reviews

The Quick Reviews (QRs) summarize a few key steps (but not all steps) needed to complete each Activity in Computer Lab 3B. These QRs will be useful when you are preparing for the computer components of the assignments, midterm exam, and final exam. To access, the QRs, click Computer Lab 3B QRs .

Self-Test 3

To access Self-Test 3, click MATH 216 Self-Test 3 .

It is important that you work through all the exercises in the unit self-tests and the e-text chapter quizzes. No grades are assigned to the self-tests. They are designed to, along with the unit assignments, help you master the content presented in each unit.

Each unit self-test has two parts: one on theory (A) and one on computer work (B). Working through these will help you review key exercises in the unit, which will help you prepare for assignments and exams.

Assignment 3

After completing Self-Test 3, complete Assignment 3, which you will find on the course home page. Submit your solutions to this assignment to your tutor for marking.

• Course Orientation
• Study Guide
• Computer Lab Guided Solutions (Technology Manual)
• Computer Lab Quick Review
• Self-Test B (Computer Component) Solutions

Mathematics 216 Computer-oriented Approach to Statistics

Study Guide :: Unit 4

Inference on one sample, introduction.

In Unit 3, you learned about the probability distribution of a random variable and how to compute the associated mean, variance, and probabilities. Numerical quantities that describe probability distributions are called parameters. In practice, because this information is not available it must be estimated using statistical techniques.

The most accurate way of obtaining information about a population parameter would be to collect the relevant data from every member of that population. Such a procedure is impractical in most cases. For example, a tire manufacturer who wanted to know the average lifespan of their tires could not stay in business if they tested every tire until it wore out. Similarly, if we wanted to know the average lifespan of Canadians, we could not wait until all members of the Canadian population had died.

Hence, the best way to gather information about a population is to collect data from a representative sample of the population and make inferences about the population. The numerical descriptive measures (such as sample mean, sample proportion, sample standard deviation, etc.) are called statistics. However, statistics vary from sample to sample. Stated simply, if we consider all possible samples from a given population, we will find variability in the sample statistic; that is, each sample statistic will have its own distribution. If all possible values of a sample statistic that might occur are organized into a probability distribution, the resulting distribution is called the sampling distribution.

This unit begins by discussing sampling distribution of means and proportions, and how the mean and standard deviation are related to the mean and standard deviation of the parent population. Central limit theorem, the foundation for the inferential branch of statistics, is introduced in this context. Once you understand the concept of sampling distributions and central limit theorem, you are ready to begin the study of inferential statistics, which is concerned with estimating a population parameter (characteristic) based on results observed from a sample.

In the rest of this unit, we discuss the two categories of inferential statistics: estimation and hypothesis testing. Estimation is the process of obtaining a single numerical value (point estimate) or a set of values (interval estimate or confidence interval) intended as a “best guess” of the unknown population parameter. In hypothesis testing, we test claims regarding a characteristic of one or more populations. The claims that we test concern the population mean and the population proportion.

• Sampling Distributions and the Central Limit Theorem

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

• Explain the term “sampling distribution” and verify its properties.
• Calculate the mean and standard deviation of the sampling distribution of sample means.
• Describe and interpret central limit theorem.
• Finding Probabilities for the Sample Mean.

Important Note : For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics , Chapter 5, Section 5.4 Sampling Distributions and the Central Limit Theorem

Try It Yourself Examples

Work through each Try It Yourself example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Do the following exercises in your eText:

Chapter 5, Section 5.4 Exercises 1, 5, 7, 9, 11, 13, 15. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 5 Section 5.4 are available on the textbook publisher’s MyLab website.

Chapter 5.4 Review ( Extra Online Practice )

For more practice working with the topics in this chapter of the eText, work through this review. Or, if you feel you have mastered this material, you may skip to the computer lab section of this unit.

Review Learning Objectives

Before proceeding to the online exercises, briefly review the Learning Objectives for the topic (below) presented in the previous section of this Study Guide:

Optional Practice in the MyLab Study Plan

For more practice on the topics/sections of this chapter of your eText, visit Pearson MyLab, and work interactively through the exercises in the Study Plan. For help accessing this resource, see Accessing Pearson MyLab on the course home page.

Confidence Intervals for the Mean ( σ Known)

• point estimate; interval estimate
• confidence interval; level of confidence
• margin of error
• Compute point estimate and margin of error for the population mean.
• Construct and interpret intervals for the population mean.
• Determine the minimum sample size required when estimating μ .

Elementary Statistics , Chapter 6, Section 6.1 Confidence Intervals for the Mean ( σ Known)

Chapter 6, Section 6.1 Exercises 3, 35, 37, 41, 49, 55. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 6, Section 6.1 are available on the textbook publisher’s MyLab website.

Confidence Intervals for the Mean ( σ Unknown)

• Interpret t distribution and use a  t- distribution table.
• Know the properties of students’ t- distribution.
• Construct confidence intervals when n < 30, the population is normally distributed, and σ is known.

Elementary Statistics , Chapter 6, Section 6.2 Confidence Intervals for the Mean ( σ Unknown)

Chapter 6, Section 6.2 Exercises 1, 3, 5, 7, 9, 13, 17, 21. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 6 Section 6.2 are available on the textbook publisher’s MyLab website.

Confidence Intervals for Population Proportions

• Obtain a point estimate for the population proportion.
• Construct and interpret confidence intervals for the population proportion.
• Determine the minimum sample size required for estimating a population proportion within a specified margin of error.

Elementary Statistics , Chapter 6, Section 6.3 Confidence Intervals for Population Proportions

Chapter 6, Section 6.3 Exercises 1, 3, 7, 13, 19, 21, 23, 25. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 6 Section 6.3 are available on the textbook publisher’s MyLab website.

Chapter 6 Review ( Extra Online Practice )

For more practice working with the topics in this chapter of the eText, work through this review. Or, if you feel you have mastered this material, you may skip to Computer Lab 4A.

Before proceeding to the online exercises, briefly review the Learning Objectives for each of the following topics (listed below), which are presented in previous sections of this Study Guide.

• Confidence Interval for Mean ( σ Known)
• Confidence Interval for Mean ( σ Unknown)
• Confidence Interval for Population Proportion

For more practice on the topics/sections of Chapter 6, visit Pearson MyLab, and work interactively through the exercises in the Study Plan. For help accessing this resource, see Accessing Pearson MyLab on the course home page.

Computer Lab 4A

In Computer Lab 4A, you will learn to use StatCrunch to develop solutions to exercises related to topics in the eText’s Chapter 5 and 6.

Computer Lab 4A Detailed Instructions

Your Computer Lab activities and the detailed step-by-step instructions (Guided Solutions) that will guide you in using StatCrunch to complete these are in the Computer Lab 4A file.

Computer Lab 4A Quick Reviews

The Quick Reviews (QRs) summarize a few key steps (but not all steps) needed to complete each Activity in Computer Lab 4A. These QRs will be useful when you are preparing for the computer components of the assignments, midterm exam, and final exam. To access the QRs, click Computer Lab 4A QRs .

• Introduction to Hypothesis Testing with One Sample
• Determine the null and alternative hypotheses from a claim.
• Distinguish between type I and type II errors.
• Interpret the level of significance.
• Determine whether to use a one-tailed or two-tailed statistical test.
• Compute and interpret  P -value.
• Make and interpret a decision based on the results of a hypothesis test.

Elementary Statistics , Chapter 7, Section 7.1 Introduction to Hypothesis Testing

Chapter 7, Section 7.1 Exercises 1, 11, 13, 15,  21, 29, 31, 33, 35, 37, 41, 43, 45, 51. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 7 Section 7.1 are available on the Pearson MyLab website.

Hypothesis Testing for the Mean ( σ Known)

• Use P -values to make decisions.
• Use P -values in a z -test.
• Construct critical (rejection) regions and critical values.
• Use rejection regions in a z -test.

Elementary Statistics , Chapter 7, Section 7.2 Hypothesis Testing for the Mean ( σ Known)

Chapter 7, Section 7.2 Exercises 1, 3, 9, 15, 19, 25, 33, 37, 39. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 7, Section 7.2 are available on the Pearson MyLab website.

Hypothesis Testing for the Mean ( σ Unknown)

• Find critical values in a t distribution.
• Apply the t -test to test a mean μ , using the critical values/rejection region approach.

Elementary Statistics , Chapter 7, Section 7.3 Hypothesis Testing for the Mean ( σ Unknown)

Chapter 7, Section 7.3 Exercises 1, 3, 9, 11, 13,  19, 21, 25, 27. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 7 Section 7.3 are available on the  Pearson MyLab website.

Note 1: Unless otherwise stated, always use the critical values/rejection region approach when using your calculator to work through hypotheses test exercises and problems in the Exercises sections of your textbook, in the unit Self-Test Theory Components, and Assignment Theory Components for the remainder of this course.

Note 2: Unless otherwise stated, always use the P -value approach when using your computer, with  StatCrunch, to work through hypotheses test exercises and problems in the Computer Labs, Unit Self-test Computer Components, and Assignment Computer Components for the remainder of this course.

• Hypothesis Testing for Proportions

Learning Objective

• Apply z in hypotheses tests involving a population proportion, using the critical values/rejection region approach.

Elementary Statistics , Chapter 7, Section 7.4 Hypothesis Testing for Proportions

Chapter 7, Section 7.4 Exercises 1,3, 5, 7, 9, 11, 13. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Additional optional multimedia resources related to Chapter 7 Section 7.4 are available on the Pearson MyLab website.

Note: Use the critical values/rejections region approach to conduct test of hypotheses exercises, using your calculator.

Chapter 7 Review ( Extra Online Practice )

For more practice working with the topics in this chapter of the eText, work through this review. Or, if you feel you have mastered this material, you may skip to Computer Lab 4B.

• Hypothesis Testing for Mean ( σ Known)
• Hypothesis Testing for Mean ( σ Unknown)

If you would like more practice on the various topics/sections of Chapter 7, you may wish to visit the website that accompanies your textbook, and work interactively through online exercises located in the Study Plan. For help accessing this resource, see Accessing Pearson MyLab on the course home page.

Computer Lab 4B

In Computer Lab 4B, you will learn to use StatCrunch to develop solutions to exercises related to topics in the eText’s Chapter 7.

Computer Lab 4B Detailed Instructions

Your Computer Lab activities and the detailed step-by-step instructions (Guided Solutions) that will guide you in using StatCrunch to complete these are in the Computer Lab 4B file.

Computer Lab 4B Quick Reviews

The Quick Reviews (QRs) summarize a few key steps (but not all steps) needed to complete each Activity in Computer Lab 4B. These QRs will be useful when you are preparing for the computer components of the assignments, midterm exam, and final exam. To access the QRs, click Computer Lab 4B QRs .

Self-Test 4

To access Self-Test 4, click MATH 216 Self-Test 4 .

It is important that you work through all the exercises in the unit self-tests and the eText chapter quizzes. No grades are assigned to the self-tests. They are designed to, along with the unit assignments, help you master the content presented in each unit.

Each unit self-test has two parts: one on theory (A) and one on computer work (B). Working through these will help you review key exercises in the unit, which will help you prepare for assignments and exams.

Assignment 4

After completing Self-Test 4, complete Assignment 4, which you will find on the course home page. Submit your solutions to this assignment for marking using the drop box on the course home page.