Statistics: 1,001 Practice Problems For Dummies

507 Pages·2014·5.75 MB·English

by  Consumer Dummies

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1,001 Statistics
Prac tice Problems
1,001 Statistics Practice Problems For Dummies®
Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
Copyright © 2014 by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Control Number: 2013954236
ISBN 978-1-118-77604-9 (pbk); ISBN 978-1-118-77605-6 (ebk); ISBN 978-1-118-77616-2 (ebk)
Manufactured in the United States of America
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Contents at a Glance
Introduction ............................................................................1
Part I: The Questions ................................................................5
Chapter 1: Basic Vocabulary ...............................................................................................................7
Chapter 2: Descriptive Statistics.......................................................................................................11
Chapter 3: Graphing ...........................................................................................................................21
Chapter 4: Random Variables and the Binomial Distribution .......................................................33
Chapter 5: The Normal Distribution .................................................................................................43
Chapter 6: The t-Distribution .............................................................................................................51
Chapter 7: Sampling Distributions and the Central Limit Theorem .............................................57
Chapter 8: Finding Room for a Margin of Error ..............................................................................71
Chapter 9: Confidence Intervals: Basics for Single Population Means and Proportions ...........75
Chapter 10: Confidence Inter vals for Two Population Means and Propor tions ........................91
Chapter 11: Claims, Tests, and Conclusions ...................................................................................97
Chapter 12: Hypothesis Testing Basics for a Single Population Mean: z- and t-Tests ..............105
Chapter 13: Hypothesis Tests for One Proportion, Two Proportions, or
Two Population Means ..................................................................................................................117
Chapter 14: Surveys ..........................................................................................................................127
Chapter 15: Correlation ....................................................................................................................131
Chapter 16: Simple Linear Regression ...........................................................................................139
Chapter 17: Two-Way Tables and Independence .........................................................................153
Part II: The Answers ............................................................165
Chapter 18: Answers.........................................................................................................................167
Appendix: Tables for Reference .............................................469
Index ..................................................................................481

Table of Contents
Introduction ................................................................. 1
What You’ll Find ..............................................................................................1
How This Workbook Is Organized .................................................................1
Part I: The Questions .............................................................................2
Part II: The Answers ..............................................................................3
Beyond the Book .............................................................................................3
What you’ll find online ..........................................................................3
How to register .......................................................................................3
Where to Go for Additional Help ...................................................................4
Part I: The Questions .................................................... 5
Chapter 1: Basic Vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
The Problems You’ll Work On .......................................................................7
What to Watch Out For ...................................................................................7
Picking Out the Population, Sample, Parameter, and Statistic ..................8
Distinguishing Quantitative and Categorical Variables ..............................8
Getting a Handle on Bias, Variables, and the Mean ....................................9
Understanding Different Statistics and Data Analysis Terms ....................9
Using Statistical Techniques ........................................................................10
Working with the Standard Deviation .........................................................10
Chapter 2: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
The Problems You’ll Work On .....................................................................11
What to Watch Out For .................................................................................11
Understanding the Mean and the Median ..................................................12
Surveying Standard Deviation and Variance ..............................................13
Employing the Empirical Rule ......................................................................15
Measuring Relative Standing with Percentiles ...........................................16
Delving into Data Sets and Descriptive Statistics ......................................17
Chapter 3: Graphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
The Problems You’ll Work On .....................................................................21
What to Watch Out For .................................................................................21
Interpreting Pie Charts .................................................................................22
Considering Three-Dimensional Pie Charts ...............................................22
Interpreting Bar Charts .................................................................................23
Introducing Other Graphs ............................................................................24
Interpreting Histograms ...............................................................................24
Digging Deeper into Histograms ..................................................................25
Comparing Histograms .................................................................................26
Describing the Center of a Distribution ......................................................27
Interpreting Box Plots ...................................................................................27
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1,001 Statistics Practice Problems For Dummies
Comparing Two Box Plots ............................................................................28
Comparing Three Box Plots .........................................................................29
Interpreting Time Charts ..............................................................................30
Getting More Practice with Histograms .....................................................31
Chapter 4: Random Variables and the Binomial Distribution . . . . . . .33
The Problems You’ll Work On .....................................................................33
What to Watch Out For .................................................................................33
Comparing Discrete and Continuous Random Variables .........................34
Understanding the Probability Distribution of a Random Variable ........35
Determining the Mean of a Discrete Random Variable .............................35
Digging Deeper into the Mean of a Discrete Random Variable ................35
Working with the Variance of a Discrete Random Variable .....................36
Putting Together the Mean, Variance, and Standard
Deviation of a Random Variable...............................................................36
Digging Deeper into the Mean, Variance, and
Standard Deviation of a Random Variable ..............................................37
Introducing Binomial Random Variables ....................................................37
Figuring Out the Mean, Variance, and Standard
Deviation of a Binomial Random Variable ..............................................38
Finding Binomial Probabilities with a Formula ..........................................38
Digging Deeper into Binomial Probabilities Using a Formula ..................39
Finding Binomial Probabilities with the Binomial Table ..........................39
Digging Deeper into Binomial Probabilities Using
the Binomial Table .....................................................................................40
Using the Normal Approximation to the Binomial ....................................40
Digging Deeper into the Normal Approximation
to the Binomial ...........................................................................................41
Getting More Practice with Binomial Variables .........................................41
Chapter 5: The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
The Problems You’ll Work On .....................................................................43
What to Watch Out For .................................................................................43
Defining and Describing the Normal Distribution .....................................44
Working with z-Scores and Values of X ......................................................45
Digging Deeper into z-Scores and Values of X ...........................................45
Writing Probability Notations ......................................................................46
Introducing the Z-Table ................................................................................47
Finding Probabilities for a Normal Distribution ........................................47
Digging Deeper into z-Scores and Probabilities ........................................47
Figuring Out Percentiles for a Normal Distribution ..................................48
Digging Deeper into Percentiles for a Normal Distribution .....................49
Getting More Practice with Percentiles ......................................................49
Chapter 6: The t-Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
The Problems You’ll Work On .....................................................................51
What to Watch Out For .................................................................................51
Understanding the t-Distribution and Comparing It
to the Z-Distribution ..................................................................................52
Using the t-Table ............................................................................................53
Using the t-Distribution to Calculate Confidence Intervals ......................55
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Table of Contents
Chapter 7: Sampling Distributions and the
Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
The Problems You’ll Work On .....................................................................57
What to Watch Out For .................................................................................57
Introducing the Basics of Sampling Distributions .....................................58
Checking Out Random Variables and Sample Means ...............................59
Examining Standard Error ............................................................................59
Surveying Notation and Symbols ................................................................60
Understanding What Affects Standard Error .............................................61
Digging Deeper into Standard Error ............................................................61
Connecting Sample Means and Sampling Distributions ...........................62
Digging Deeper into Sampling Distributions of Sample Means .................64
Looking at the Central Limit Theorem ........................................................65
Getting More Practice with Sample Mean Calculations ............................66
Finding Probabilities for Sample Means .....................................................66
Digging Deeper into Probabilities for Sample Means ................................67
Adding Proportions to the Mix ....................................................................68
Figuring Out the Standard Error of the Sample Proportion .....................68
Using the Central Limit Theorem for Proportions ....................................68
Matching z-Scores to Sample Proportions .................................................69
Finding Approximate Probabilities .............................................................69
Getting More Practice with Probabilities ...................................................69
Digging Deeper into Approximate Probabilities ........................................70
Chapter 8: Finding Room for a Margin of Error . . . . . . . . . . . . . . . . . . . .71
The Problems You’ll Work On .....................................................................71
What to Watch Out For .................................................................................71
Defining and Calculating Margin of Error ...................................................72
Using the Formula for Margin of Error When
Estimating a Population Mean ..................................................................72
Finding Appropriate z*-Values for Given Confidence Levels ...................73
Connecting Margin of Error to Sample Size ...............................................73
Getting More Practice with the Formula for Margin of Error ..................73
Linking Margin of Error and Population Proportion .................................74
Chapter 9: Confidence Intervals: Basics for Single
Population Means and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75
The Problems You’ll Work On .....................................................................75
What to Watch Out For .................................................................................75
Introducing Confidence Intervals ................................................................76
Checking Out Components of Confidence Intervals .................................76
Interpreting Confidence Intervals ................................................................79
Spotting Misleading Confidence Intervals ......................................................80
Calculating a Confidence Interval for a Population Mean ........................83
Determining the Needed Sample Size .........................................................86
Introducing a Population Proportion ..........................................................87
Connecting a Population Proportion to a Survey ......................................88
Calculating a Confidence Interval for a Population Proportion ..............88
Digging Deeper into Population Proportions .............................................89
Getting More Practice with Population Proportions ................................90
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1,001 Statistics Practice Problems For Dummies
Chapter 10: Confidence Inter vals for Two
Population Means and Propor tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
The Problems You’ll Work On .....................................................................91
What to Watch Out For .................................................................................91
Working with Confidence Intervals and
Population Proportions .............................................................................92
Digging Deeper into Confidence Intervals and
Population Proportions .............................................................................92
Working with Confidence Intervals and Population Means ...........................93
Making Calculations When Population Standard
Deviations Are Known .....................................................................................93
Digging Deeper into Calculations When Population
Standard Deviations Are Known ..............................................................94
Working with Unknown Population Standard
Deviations and Small Sample Sizes ..........................................................95
Digging Deeper into Unknown Population Standard
Deviations and Small Sample Sizes ...............................................................95
Chapter 11: Claims, Tests, and Conclusions . . . . . . . . . . . . . . . . . . . . . .97
The Problems You’ll Work On .....................................................................97
What to Watch Out For .................................................................................97
Knowing When to Use a Hypothesis Test ...................................................98
Setting Up Null and Alternative Hypotheses ..............................................98
Finding the Test Statistic and the p-Value ................................................100
Making Decisions Based on Alpha Levels and Test Statistics ...............101
Making Conclusions ....................................................................................101
Understanding Type I and Type II Errors .................................................103
Chapter 12: Hypothesis Testing Basics for a Single
Population Mean: z- and t-Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
The Problems You’ll Work On ...................................................................105
What to Watch Out For ...............................................................................105
Knowing What You Need to Run a z-Test .................................................106
Determining Null and Alternative Hypotheses ........................................106
Introducing p-Values ...................................................................................107
Calculating the z-Test Statistic ..................................................................107
Finding p-Values by Doing a Test of One Population Mean ...................108
Drawing Conclusions about Hypotheses ..................................................108
Digging Deeper into p-Values .....................................................................109
Digging Deeper into Conclusions about Hypotheses ..............................109
Digging Deeper into Null and Alternative Hypotheses ...........................110
Knowing When to Use a t-Test ...................................................................111
Connecting Hypotheses to t-Tests .............................................................111
Calculating Test Statistics ..........................................................................112
Working with Critical Values of t ...............................................................112
Linking p-Values and t-Tests .......................................................................113
Drawing Conclusions from t-Tests .............................................................114
Performing a t-Test for a Single Population Mean ...................................115
Drawing More Conclusions from t-Tests ..................................................115