Designed by Engin A. Sungur

Lesson 6 & 7:

Contents

This sixth and seventh lessons cover ...

Objectives

After completing this lesson, you should be able to learn the following:

6. Introduction to Inference

6.1 Estimating with Confidence

  • Constructing a level C confidence interval for the population mean m

  • Understanding and interpreting confidence intervals

  • Determination of sample size for a given margin of error for the population

mean m

6.2 Tests of Significance

  • Setting up null and alternative hypotheses

  • Finding and interpreting a P-value

  • Understanding tests with fixed significance level

  • 6.3 Use and Abuse of Tests (excluding Power and Inference as Decision)

  • Finding the Power of a test

  • Inference as decision

7. Inference for Distributions

7.1 Inference for the Mean of a Population Mean

  • Understanding t distribution and being able to use the t-tables

  • Setting up a confidence interval for m when s is unknown (assumptions)

  • Testing a hypothesis for m when s is unknown (assumptions) (P-value or fixed significance level)

  • Finding the power of t test

  • Making inference for nonnormal populations

  • 7.2 Comparing two means

  • 7.3 (Not included)

 

Reading Assignment

Read chapters 6 & 7 in Introduction to the Practice of Statistics.

Activities

Let Us Toss a Coin

Key Terms

Chapters 6 & 7

Chapter 6 & 7: Study Questions

  1. What is a confidence interval?
  2. What is a test of hypothesis?
  3. What are the similarities and differences between test of hypothesis and confidence interval?
  4. What is the difference between z and t procedures?
  5. What is the meaning of a P-value?
  6. What is the significance level?
  7. What is the power of a test?

Chapter 6 & 7: Study Notes


To complement your text, we will present the following tables that may help you to put every thing you have learned together.
For a test of hypothesis problem always go over the following steps
  1. Set up your null and alternative hypothesis
  2. Select the significance level of the test
  3. Decide which test statistics you need to use
  4. Find the value of your test statistic and P-value
  5. Write down your decision

If you want to make an inference related with a single population mean use the following two tables. Note that first you need to figure out whether or not the population standard deviation is known.

Inference on Population Mean

(Population Standard Deviation Known)

Test Of Hypothesis

Null & Alternative Hypothesis

Significance Level Of the Test

a

a

a

Test Statistics

p-value

Table A

Table A

Table A

Decision

Confidence Interval

(get the z* value from the Table D)

Determination of the Sample Size

(get the z* value from the Table D, m is the margin of error)

Inference on Population Mean

(Population Standard Deviation Unknown)

Test Of Hypothesis

Null & Alternative Hypothesis

Significance Level Of the Test

a

a

a

Test Statistics

p-value

Table E

with d.f.=n-1

Table E

with d.f.=n-1

Table E

with d.f.=n-1

Decision

Confidence Interval

(get the t* value from the Table E with degrees of freedom n-1)

If you want to make an inference related with comparing two population mean use the following two tables. Note that first you need to figure out whether or not the population standard deviations are known.

Inference on Difference Between Population Means

(Population Standard Deviations Known)

Test Of Hypothesis

Null & Alternative Hypothesis

Significance Level Of the Test

a

a

a

Test Statistics

p-value

Table A

Table A

Table A

Decision

Confidence Interval

(Get z* value from the Table D)

Inference on Difference Between Population Means

(Population Standard Deviations Unknown)

Test Of Hypothesis

Null & Alternative Hypothesis

Significance Level Of the Test

a

a

a

Test Statistics

p-value

Table E with d.f.

Table E with d.f.

Table E with d.f.

Decision

Confidence Interval

(Get t* value from the Table E with d.f. )

OR

Test Of Hypothesis

Null & Alternative Hypothesis

Significance Level Of the Test

a

a

a

Test Statistics

 

p-value

Table E

with

d.f.=

Table E

with

d.f.=

Table E

with

d.f.=

Decision

Confidence Interval

(Get t* value from the Table E with d.f. )

Written Assignment

Do the following assignment. The problems listed are from "Introduction to the Practice of Statistics". When you have worked on the problems and are ready to turn in your findings, click the assignment link below. It will take you to a template where you can fill in your answers to the questions. When you are finished entering your answers, click the submit button, you will be given the location of your completed web page. You may check your assignment responses with your browser at any time, and submit a revision at any time before the due date of the assignment. The due date is Friday August 13..

SECTION 6.1.Exercise 6.2, 6.10, 6.14, 6.18 (page 447-451)
SECTION 6.2.Exercises 6.28, 6.36, 6.48 (pages 468-475)
SECTION 6.4.Exercises 6.70(page 495)
SECTION 7.1.Exercise 7.4, 7.14, 7.32 (page 523-531)
SECTION 7.2.Exercises 7.48, 7.70 (pages 556-565)
CHAPTER EXERCISES.Exercises 7.100 (page 577)

Lesson Submission 6 & 7

Assignment #6.

Internet Links

Each day you go online, be sure to check out the Random Statistical Quote for the Day