INSTRUCTORS SOLUTION MANUAL JAMES LAPP A
PATHWAY TO INTRODUCTORY STATISTICS 2ND
EDITION JAY LEHMANN
Table of Contents
Chapter 1: Performing Operations and Evaluating Expressions
1.1 Variables, Constants, Plotting Points, and Inequalities ................................................................ 1
1.2 Expressions ................................................................................................................................... 4
1.3 Operations with Fractions and Proportions; Converting Units ..................................................... 7
1.4 Absolute Value and Adding Real Numbers ................................................................................ 11
1.5 Change in a Quantity and Subtracting Real Numbers ................................................................ 14
1.6 Ratios, Percents, and Multiplying and Dividing Real Numbers ................................................. 16
1.7 Exponents, Square Roots, Order of Operations, and Scientific Notation ................................... 20
Review Exercises ....................................................................................................................... 24
Chapter Test ............................................................................................................................... 27
Chapter 2: Designing Observational Studies and Experiments
2.1 Simple Random Sampling .......................................................................................................... 31
2.2 Systematic, Stratified, and Cluster Sampling ............................................................................. 34
2.3 Observational Studies and Experiments ..................................................................................... 36
Review Exercises ....................................................................................................................... 40
Chapter Test ............................................................................................................................... 43
Chapter 3: Graphical and Tabular Displays of Data
3.1 Frequency Tables, Relative Frequency Tables, and Bar Graphs ................................................ 45
3.2 Pie Charts and Two-Way Tables ................................................................................................ 49
3.3 Dotplots, Stemplots, and Time-Series Plots ............................................................................... 52
3.4 Histograms.................................................................................................................................. 58
3.5 Misleading Graphical Displays of Data ...................................................................................... 64
Review Exercises ....................................................................................................................... 66
Chapter Test ............................................................................................................................... 71
Chapter 4: Summarizing Data Numerically
4.1 Measures of Center ..................................................................................................................... 75
4.2 Measures of Spread .................................................................................................................... 80
4.3 Boxplots ..................................................................................................................................... 85
Review Exercises ....................................................................................................................... 90
Chapter Test ............................................................................................................................... 92
Chapter 5: Computing Probabilities
5.1 Meaning of Probability ............................................................................................................... 95
5.2 Complement and Addition Rules ............................................................................................... 97
5.3 Conditional Probability and the Multiplication Rule for Independent Events .......................... 100
5.4 Discrete Random Variables ...................................................................................................... 103
5.5 Finding Probabilities for a Normal Distribution ....................................................................... 106
5.6 Finding Values of Variables for Normal Distributions ............................................................. 110
Review Exercises ..................................................................................................................... 112
Chapter Test ............................................................................................................................. 114
Chapter 6: Describing Associations of Two Variables Graphically
6.1 Scatterplots ............................................................................................................................... 117
6.2 Determining the Four Characteristics of an Association .......................................................... 121
6.3 Modeling Linear Associations .................................................................................................. 125
,Review Exercises ..................................................................................................................... 130
Chapter Test ............................................................................................................................. 133
,Chapter 7: Graphing Equations of Lines and Linear Models; Rate of Change
7.1 Graphing Equations of Lines and Linear Models ..................................................................... 135
7.2 Rate of Change and Slope of a Line ......................................................................................... 138
7.3 Using Slope to Graph Equations of Lines and Linear Models .................................................. 142
7.4 Functions .................................................................................................................................. 148
Review Exercises...................................................................................................................... 152
Chapter Test ............................................................................................................................. 156
Chapter 8: Solving Linear Equations and Inequalities to Make Prediction
8.1 Simplifying Expressions ........................................................................................................... 159
8.2 Solving Linear Equations in One Variable ............................................................................... 161
8.3 Solving Linear Equations to Make Predictions ........................................................................ 163
8.4 Solving Formulas ..................................................................................................................... 170
8.5 Solving Linear Inequalities to Make Predictions ...................................................................... 175
Review Exercises...................................................................................................................... 181
Chapter Test ............................................................................................................................. 186
Chapter 9: Finding Equations of Linear Models
9.1 Using Two Points to Find an Equation of a Line...................................................................... 191
9.2 Using Two Points to Find an Equation of a Linear Model ....................................................... 193
9.3 Linear Regression Model.......................................................................................................... 198
Review Exercises...................................................................................................................... 204
Chapter Test ............................................................................................................................. 207
Chapter 10: Using Exponential Models to Make Predictions
10.1 Integer Exponents ..................................................................................................................... 209
10.2 Rational Exponents ................................................................................................................... 211
10.3 Graphing Exponential Models .................................................................................................. 213
10.4 Using Two Points to Find an Equation of an Exponential Model............................................. 216
10.5 Exponential Regression Model ................................................................................................. 221
Review Exercises...................................................................................................................... 226
Chapter Test ............................................................................................................................. 230
, Chapter 1: Performing Operations and Evaluating Expressions 1
Chapter 1: Performing Operations and Evaluating Expressions
Homework 1.1
2. A constant is a symbol that represents a specific number.
4. Data are quantities or categories that describe people, animals, or things.
6. In 2017, about 37% of children aged 6–12 participated in a team sport (organized or unorganized) on a regular
basis.
8. The temperature is 10F . That is, the temperature is 10 degrees below 0 (in Fahrenheit).
10. The statement t 3 represents the year 2012 (3 years before 2015).
12. Answers may vary. Example: Let s be the annual salary (in thousands of dollars) of a person. Then s can
represent the numbers 25 and 32, but s cannot represent the numbers 15 and 9 .
14. Answers may vary. Example: Let n be the number of students enrolled in a prestatistics class. Then n can
represent the numbers 15 and 28, but n cannot represent the numbers 20 or 0.5.
16. Answers may vary. Example: Let T be the temperature (in degrees Fahrenheit) in an oven. Then T can
represent the numbers 300 and 450, but T cannot represent the numbers 300 or 450 .
18. a. Answers may vary. Some possible answers are shown below.
b. In the described situation, the symbols W and L are variables. Their values can change.
c. In the described situation, the symbol A is a constant. Its value is fixed at 36 square feet.
20. a. Answers may vary. Some possible answers are shown below.
b. In the described situation, the symbols W, L, and A are all variables. All their values can change.
c. In the described situation, none of the symbols are constants. All their values can change.
22. 30. The integers between 6 and 3, inclusive, are
6, 5, 4, 3, 2, 1, 0, 1, 2, and 3.
24.
26.
32.
28. The counting numbers between 1 and 5 are 2, 3, 34. The positive integers between 4 and 4 are 1,
and 4. 2, and 3.
36. Answers may vary. Example: 2, 5 and 40 . 38. Answers may vary. Example: 2.1, 2.3, and
2.8 .
40. The temperature at the top of a skyscraper can be positive or negative, depending on the location of the
skyscraper and the time of year. Temperature is not usually reported using fractions. So, among the choices,
the integers are the smallest group of number that contains possible data.
PATHWAY TO INTRODUCTORY STATISTICS 2ND
EDITION JAY LEHMANN
Table of Contents
Chapter 1: Performing Operations and Evaluating Expressions
1.1 Variables, Constants, Plotting Points, and Inequalities ................................................................ 1
1.2 Expressions ................................................................................................................................... 4
1.3 Operations with Fractions and Proportions; Converting Units ..................................................... 7
1.4 Absolute Value and Adding Real Numbers ................................................................................ 11
1.5 Change in a Quantity and Subtracting Real Numbers ................................................................ 14
1.6 Ratios, Percents, and Multiplying and Dividing Real Numbers ................................................. 16
1.7 Exponents, Square Roots, Order of Operations, and Scientific Notation ................................... 20
Review Exercises ....................................................................................................................... 24
Chapter Test ............................................................................................................................... 27
Chapter 2: Designing Observational Studies and Experiments
2.1 Simple Random Sampling .......................................................................................................... 31
2.2 Systematic, Stratified, and Cluster Sampling ............................................................................. 34
2.3 Observational Studies and Experiments ..................................................................................... 36
Review Exercises ....................................................................................................................... 40
Chapter Test ............................................................................................................................... 43
Chapter 3: Graphical and Tabular Displays of Data
3.1 Frequency Tables, Relative Frequency Tables, and Bar Graphs ................................................ 45
3.2 Pie Charts and Two-Way Tables ................................................................................................ 49
3.3 Dotplots, Stemplots, and Time-Series Plots ............................................................................... 52
3.4 Histograms.................................................................................................................................. 58
3.5 Misleading Graphical Displays of Data ...................................................................................... 64
Review Exercises ....................................................................................................................... 66
Chapter Test ............................................................................................................................... 71
Chapter 4: Summarizing Data Numerically
4.1 Measures of Center ..................................................................................................................... 75
4.2 Measures of Spread .................................................................................................................... 80
4.3 Boxplots ..................................................................................................................................... 85
Review Exercises ....................................................................................................................... 90
Chapter Test ............................................................................................................................... 92
Chapter 5: Computing Probabilities
5.1 Meaning of Probability ............................................................................................................... 95
5.2 Complement and Addition Rules ............................................................................................... 97
5.3 Conditional Probability and the Multiplication Rule for Independent Events .......................... 100
5.4 Discrete Random Variables ...................................................................................................... 103
5.5 Finding Probabilities for a Normal Distribution ....................................................................... 106
5.6 Finding Values of Variables for Normal Distributions ............................................................. 110
Review Exercises ..................................................................................................................... 112
Chapter Test ............................................................................................................................. 114
Chapter 6: Describing Associations of Two Variables Graphically
6.1 Scatterplots ............................................................................................................................... 117
6.2 Determining the Four Characteristics of an Association .......................................................... 121
6.3 Modeling Linear Associations .................................................................................................. 125
,Review Exercises ..................................................................................................................... 130
Chapter Test ............................................................................................................................. 133
,Chapter 7: Graphing Equations of Lines and Linear Models; Rate of Change
7.1 Graphing Equations of Lines and Linear Models ..................................................................... 135
7.2 Rate of Change and Slope of a Line ......................................................................................... 138
7.3 Using Slope to Graph Equations of Lines and Linear Models .................................................. 142
7.4 Functions .................................................................................................................................. 148
Review Exercises...................................................................................................................... 152
Chapter Test ............................................................................................................................. 156
Chapter 8: Solving Linear Equations and Inequalities to Make Prediction
8.1 Simplifying Expressions ........................................................................................................... 159
8.2 Solving Linear Equations in One Variable ............................................................................... 161
8.3 Solving Linear Equations to Make Predictions ........................................................................ 163
8.4 Solving Formulas ..................................................................................................................... 170
8.5 Solving Linear Inequalities to Make Predictions ...................................................................... 175
Review Exercises...................................................................................................................... 181
Chapter Test ............................................................................................................................. 186
Chapter 9: Finding Equations of Linear Models
9.1 Using Two Points to Find an Equation of a Line...................................................................... 191
9.2 Using Two Points to Find an Equation of a Linear Model ....................................................... 193
9.3 Linear Regression Model.......................................................................................................... 198
Review Exercises...................................................................................................................... 204
Chapter Test ............................................................................................................................. 207
Chapter 10: Using Exponential Models to Make Predictions
10.1 Integer Exponents ..................................................................................................................... 209
10.2 Rational Exponents ................................................................................................................... 211
10.3 Graphing Exponential Models .................................................................................................. 213
10.4 Using Two Points to Find an Equation of an Exponential Model............................................. 216
10.5 Exponential Regression Model ................................................................................................. 221
Review Exercises...................................................................................................................... 226
Chapter Test ............................................................................................................................. 230
, Chapter 1: Performing Operations and Evaluating Expressions 1
Chapter 1: Performing Operations and Evaluating Expressions
Homework 1.1
2. A constant is a symbol that represents a specific number.
4. Data are quantities or categories that describe people, animals, or things.
6. In 2017, about 37% of children aged 6–12 participated in a team sport (organized or unorganized) on a regular
basis.
8. The temperature is 10F . That is, the temperature is 10 degrees below 0 (in Fahrenheit).
10. The statement t 3 represents the year 2012 (3 years before 2015).
12. Answers may vary. Example: Let s be the annual salary (in thousands of dollars) of a person. Then s can
represent the numbers 25 and 32, but s cannot represent the numbers 15 and 9 .
14. Answers may vary. Example: Let n be the number of students enrolled in a prestatistics class. Then n can
represent the numbers 15 and 28, but n cannot represent the numbers 20 or 0.5.
16. Answers may vary. Example: Let T be the temperature (in degrees Fahrenheit) in an oven. Then T can
represent the numbers 300 and 450, but T cannot represent the numbers 300 or 450 .
18. a. Answers may vary. Some possible answers are shown below.
b. In the described situation, the symbols W and L are variables. Their values can change.
c. In the described situation, the symbol A is a constant. Its value is fixed at 36 square feet.
20. a. Answers may vary. Some possible answers are shown below.
b. In the described situation, the symbols W, L, and A are all variables. All their values can change.
c. In the described situation, none of the symbols are constants. All their values can change.
22. 30. The integers between 6 and 3, inclusive, are
6, 5, 4, 3, 2, 1, 0, 1, 2, and 3.
24.
26.
32.
28. The counting numbers between 1 and 5 are 2, 3, 34. The positive integers between 4 and 4 are 1,
and 4. 2, and 3.
36. Answers may vary. Example: 2, 5 and 40 . 38. Answers may vary. Example: 2.1, 2.3, and
2.8 .
40. The temperature at the top of a skyscraper can be positive or negative, depending on the location of the
skyscraper and the time of year. Temperature is not usually reported using fractions. So, among the choices,
the integers are the smallest group of number that contains possible data.
