Mathematics 216 Computer-oriented Approach to Statistics
Study Guide :: Unit 5
Inference on Two Samples
Introduction
In Unit 4, you were introduced to important and fundamental concepts of statistical inference: estimation, and hypothesis testing. Both involved methods that used single samples, to make inferences about single population parameters.
In reality, we are not confined to single samples. There are situations in which we make use of two samples to compare two populations. For example, a researcher might wish to compare two sample means, using experimental and control groups. Or the average lifespan of two brands of light bulbs might be compared to see if their lifespans are different. Or an educational researcher might want to know whether there is variability between male and female students in their scores on mathematics achievement tests. In this unit, the inference methods that were presented in Unit 4 are slightly modified to allow the comparison of two population parameters.
Testing the Difference between Means (Independent Samples σ1, σ2 Known)
Learning Objectives
After completing the readings and exercises assigned for this topic, you should be able to:
- Explain the meaning of the key terms:
- dependent samples, independent samples
- sampling distribution of the difference of two sample means.
- Perform a two-sample z-test for the difference between two means.
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 8, Section 8.1 Testing the Difference Between Means (Independent Samples, σ1 and σ2 Known)
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 8, Section 8.1 Exercises 1, 5, 7, 11, 13, 21, 25. 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 8 Section 8.1 are available on the textbook publisher’s MyLab website.
Testing the Difference Between Means (Independent Samples σ1, σ2 Unknown)
Learning Objectives
After completing the readings and exercises assigned for this topic, you should be able to:
- Compute a pooled estimate of the standard deviation.
- Perform a t-test for the difference between two population means using small independent samples.
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 8, Section 8.2 Testing the Difference Between Means (Independent Samples, σ1 and σ2 Unknown)
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 8, Section 8.2 Exercises 1, 3, 5, 11, 15, 17, 19. 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 8 Section 8.2 are available on the textbook publisher’s MyLab website.
Testing the Difference Between Means (Dependent Samples)
Learning Objective
After completing the readings and exercises assigned for this topic, you should be able to achieve the following learning objective.
- Perform a t-test to test the mean of the differences for a population of paired data.
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 8, Section 8.3 Testing the Difference Between Means (Dependent Samples)
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 8, Section 8.3 Exercises 1, 3, 5, 7, 11, 15, 19 (pages 442-446). 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 8 Section 8.3 are available on the textbook publisher’s MyLab website.
Testing the Difference Between Proportions
Learning Objectives
After completing the readings and exercises assigned for this topic, you should be able to:
- Compute a weighted estimate of p1 and p2.
- Describe the sampling distribution of the difference between sample proportions.
- Perform a z-test for the difference between two population proportions.
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 8, Section 8.4 Testing the Difference Between Proportions
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 8, Section 8.4 Exercises 1, 3, 7, 13, 17. 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 8 Section 8.4 are available on the textbook publisher’s MyLab website.
Chapter 8 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 each of the topics (listed below), which are presented in previous sections of this Study Guide:
- Testing the difference between means (σ1, σ2 Known)
- Testing the difference between means (σ1, σ2 Unknown)
- Testing the difference between means (Dependent samples)
- Testing the difference between proportions
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.
Computer Lab 5
In Computer Lab 5, you will learn to use StatCrunch to develop solutions to exercises related to hypothesis tests involving two samples, most of which is from Chapter 8 of your eText.
To view all of the Computer Lab 5 exercises and the detailed step-by-step instructions that will guide you to use StatCrunch to complete these exercises, see Computer Lab 5.
Self-Test 5
To access Self-Test 5, click MATH 216 Self-Test 5.
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 5
After completing Self-Test 5, complete Assignment 5, 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.