Contents at a Glance
Part I: The Questions
Basic Vocabulary
Descriptive Statistics
Graphing
Random Variables and the Binomial Distribution
The Normal Distribution
The t-Distribution
Sampling Distributions and the Central Limit Theorem
Finding Room for a Margin of Error
Confidence Intervals: Basics for Single Population Means and Proportions
Confidence Inter vals for Two Population Means and Propor tions
Claims, Tests, and Conclusions
Hypothesis Testing Basics for a Single Population Mean: z- and t-Tests
Hypothesis Tests for One Proportion, Two Proportions, or
Two Population Means
Surveys
Correlation
Simple Linear Regression
Two-Way Tables and Independence
Part II: The Answers
Answers
Appendix: Tables for Reference
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Book Details
Price
|
2.50 |
|---|---|
Pages
| 507 p |
File Size
|
5,884 KB |
File Type
|
PDF format |
ISBN
| 978-1-118-77604-9 (pbk) 978-1-118-77605-6 (ebk) 978-1-118-77616-2 (ebk) |
Copyright©
| 2014 by John Wiley & Sons, Inc |
One thousand and one practice problems for statistics! That’s probably more than a
professor would assign you in one semester (we hope!). And it’s more than you’d ever
want to tackle in one sitting (and we don’t recommend you try). So why so many practice
problems, and why this book?
Many textbooks are pretty thin on exercises, and even those that do contain a fair number
of problems can’t focus on all aspects of each topic. With so many problems available in
this book, you get to choose how many problems you want to work on. And the way these
problems are organized helps you quickly find and dig into problems on particular topics
you need to study at the time. Whether you’re into the normal distribution, hypothesis
tests, the slope of a regression line, or histograms, it’s all here and easy to find.
Then there’s the entertainment factor. What better way to draw a crowd than to invite
people over for a statistics practice problems marathon!
What You’ll Find
This book contains 1,001 statistics problems divided into 17 chapters, organized by the
major statistical topics in a first-semester introductory course. The problems basically take
on three levels:
✓ Statistical literacy: Understanding the basic concepts of the topic, including terms and notation
✓ Reasoning: Applying the ideas within a context
✓ Thinking: Putting ideas and concepts together to solve more difficult problems
In addition to providing plenty of problems to work on in each chapter, this book also provides
worked-out solutions with detailed explanations, so you aren’t left high and dry if you
get a wrong answer. So you can rest assured that when you work for 30 minutes on a problem,
get an answer of 1.25, and go to the back of the book to see that the correct answer is
actually 1,218.31, you’ll find a detailed explanation to help you figure out what went wrong
with your calculations.
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
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
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
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
Chapter 13: Hypothesis Tests for One Proportion,
Two Proportions, or Two Population Means . 117
The Problems You’ll Work On....................................................................117
What to Watch Out For................................................................................117
Testing One Population Proportion...........................................................118
Comparing Two Independent Population Means.....................................120
Digging Deeper into Two Independent Population Means......................121
Getting More Practice with Two Independent Population Means.........121
Using the Paired t-Test.................................................................................122
Digging Deeper into the Paired t-Test........................................................123
Comparing Two Population Proportions..................................................124
Digging Deeper into Two Population Proportions...................................124
Chapter 14: Surveys . 127
The Problems You’ll Work On....................................................................127
What to Watch Out For................................................................................127
Planning and Designing Surveys.................................................................128
Selecting Samples and Conducting Surveys..............................................128
Chapter 15: Correlation . 131
The Problems You’ll Work On....................................................................131
What to Watch Out For................................................................................131
Interpreting Scatter Plots............................................................................132
Creating Scatter Plots..................................................................................132
Understanding What Correlations Indicate..............................................133
Digging Deeper into Scatter Plots...............................................................133
Digging Deeper into What Correlations Indicate......................................134
Calculating Correlations..............................................................................134
Noting How Correlations Can Change.......................................................135
Looking at the Properties of Correlations.................................................135
Digging Deeper into How Correlations Can Change.................................136
Making Conclusions about Correlations...................................................136
Getting More Practice with Scatter Plots and Correlation Changes......136
Making More Conclusions about Correlations.........................................137
Chapter 16: Simple Linear Regression 139
The Problems You’ll Work On....................................................................139
What to Watch Out For................................................................................139
Introducing the Regression Line................................................................140
Knowing the Conditions for Regression....................................................140
Examining the Equation for Calculating the
Least-Squares Regression Line................................................................140
Finding the Slope and y-Intercept of a Regression Line...........................141
Seeing How Variables Can Change in a Regression Line.........................141
Finding a Regression Line............................................................................141
Digging Deeper into Finding a Regression Line........................................142
Connecting to Correlation and Linear Relationships...............................144
Determining Whether Variables Are Candidates
for a Linear Regression Analysis.............................................................144
Digging Deeper into Correlations and Linear Relationships...................145
Describing Linear Relationships.................................................................145
Getting More Practice with Finding a Regression Line............................146
Making Predictions.......................................................................................147
Figuring Out Expected Values and Differences.........................................148
Digging Deeper into Expected Values and Differences............................149
Digging Deeper into Predictions.................................................................150
Getting More Practice with Expected Values and Differences...............150
Chapter 17: Two-Way Tables and Independence . 153
The Problems You’ll Work On....................................................................153
What to Watch Out For................................................................................153
Introducing Variables and Two-Way Tables.............................................154
Reading a Two-Way Table...........................................................................154
Interpreting a Two-Way Table by Using Percentages..............................156
Interpreting a Two-Way Table by Using Counts.......................................156
Connecting Conditional Probabilities to Two-Way Tables............................ 157
Investigating Independent Variables.........................................................158
Calculating Marginal Probability and More..............................................159
Adding Joint Probability to the Mix...........................................................160
Digging Deeper into Conditional and Marginal Probabilities.................161
Figuring Out the Number of Cells in a Two-Way Table............................162
Including Conditional Probability..............................................................162
Digging into Research Designs....................................................................163
Digging Deeper into Two-Way Tables........................................................163
Part II: The Answers.................................................. 165
Chapter 18: Answers . 167
Appendix: Tables for Reference................................... 469
Index........................................................................ 481
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Beyond the Book
This book of 1,001 practice problems will keep you busy with pencil and paper for a while,
but like the infomercials say, “Wait! There’s more!” Your book purchase also comes with a
free, one-year subscription to all 1,001 practice problems online. Track your progress and
view personalized reports that show where you need to study the most and what you’re
pretty comfortable with.