Index of Applications
Ex: Example; AEx: Applied Example; CPT: Chapter Practice Test.
All others are exercises.
Agriculture
Cherry orchard yields: 9.155
Circumferences of oranges: 9.149
Corrosive effects of soil: 10.27
Diameters of Red Delicious apples: 7.50, 7.51
Diameters of tomatoes: 9.180
Farm real estate values: 9.139
Germination trials: 5.123, 5.124
Grapefruit characteristics: 4.147, CPT 8.15
Growth of hybrid plants by soil type: CPT 11.14
Magnesium and calcium in Russian wild rye: 13.77
Maturity time of green beans: 9.138
Nitrogen fertilizer and wheat production: 13.85,
CPT 13.11, CPT 13.12, CPT 13.13, CPT 13.14,
CPT 13.15, CPT 13.16, CPT 13.17, CPT 13.18,
CPT 13.19, CPT 13.20, CPT 13.21
Number of stamens and carpels in flowers: 13.83
Oat crop yields: 9.158, 10.162, 12.28
Peanut yield rate: 14.6, 14.36
Petal and sepal measurements of irises: 3.27
Petal width of irises: 12.53
Strontium distribution coefficient and total aluminum
for soils: 13.53
Sucrose percentages in sugar cane and sugar beets:
10.121, 10.144, 13.40
Sugar cane production: 3.99
Sunflower yields: 10.49
Sweet corn yields: 10.126
Tree growth: 10.6
Tree survival: 5.61
Watermelon weights: 6.59
Weight gains for chicks: 2.157
Weight gains for pigs: 10.20
Weights of poultry flock: 9.27
Wheat production: 13.1, 13.2, 13.91
World cocoa production: 2.16
Yields of hops: 2.109
Biological Science
Animals’ brain lengths and weights: 13.22
Brown trout lengths: 2.191
Cayuga Lake fish lengths: 8.35
Cricket chirp rate and temperature: 3.96
Distribution and abundance of sea otters: AEx 14.8
Lake trout lengths: CPT 7.11
Length and age of blacknose dace: 3.94
Length and weight of alligators: 3.98
Length and weight of bears: 13.6
Lengths of hatchery-raised trout: 8.173
Long-haired rabbits: 5.70
Manatee deaths in Florida: 3.37, 11.31
Mendelian theory of inheritance: Ex 11.2, 11.12, 11.13,
11.15, 11.47
Nutrient loads discharged into Biscayne Bay: AEx 13.11,
13.66
Shark attacks: AEx 1.4
Weight and girth of horses: 13.12
Weight and length of adult cicadas: 3.101, 12.54, 13.64
Weight gain of laboratory mice: 10.71, CPT 14.12
Weights of bees’ loads of pollen and nectar: 8.183
Business, Economics, and Financial Management
Accuracy of tax withholding: 11.50
Ages and prices of Honda Accords: 3.72
American Express card fees: 6.111
Amounts in medical flexible spending accounts: 8.150
Amounts spent on veterinary care: 7.52
Annual fuel consumption: 8.187
Auto repair charges: 8.87, 10.10
Average home size: 8.116
Best companies to work for: 5.7
Burden of proof in tax dispute cases: 10.157
Carat weight and price of diamonds: 13.45
Checkout times: 1.12, CPT 2.11, 8.115, 8.185
Commissioned sales amounts: 8.18
Commute times: 8.188, 10.21, 12.1, 12.2, 12.62, Ex 14.2
Commuting distances: 2.160
Commuting distances and times: Ex 13.5, Ex 13.6,
Ex 13.8, 13.59, Ex 13.9, Ex 13.10, 13.65
Company dress codes: 2.5
Company spending on travel: 3.4
Compensation by type of organization: 1.4
Costs of luxury cars and “feel alike” models: 3.70
County transfer taxes: 12.46
Credit card rewards and rebates: 9.77
Customer accounts at banks: 9.72
Delivery service fees: 2.25
Earnings per share for banking industry: 2.186
Earnings per share for radio industry: 2.223
Emergency funds available by gender: 3.82
Entertainment sports industry salaries: 4.65
Executive salaries: 6.46
Executives’ job search: 1.72
Expected payoff from investment: 5.125
Franchised restaurant sales: 9.179
Gas-tax money by region: 12.44
GDP and level of technology: 13.20
Gold-collar workers: 6.50
Home values in college town: 9.48
Home values in Rochester suburbs: 10.73
Hourly earnings by industry: 2.196
Hourly wages of production workers: 12.35
Hours worked by Java professionals: 1.3
House selling prices: 2.18, 10.62
Illegal tax deductions: 4.75
Jeans inventories in Levi Strauss stores: 9.49
Job growth percentage changes: 14.83
Job interview outcomes: 4.149
Leasable office space available: 6.62
Life insurance purchases: 4.113
Life insurance rates: AEx 3.6, 3.49, 3.75, Ex 4.6
Losses from online identity theft: 8.166
Magazine subscription rates: 3.35
Making business decisions: 4.119
Minimum deposit and interest rate: 3.10
Monthly car payments: 2.222
Mortgage foreclosures: 5.75
Motor-fuel taxes: 3.65
Number of client contacts and sales volume: 13.41
Numbers of automobiles by country: 4.143
Obesity and productivity: AEx 1.3
“On-hold” times for customer service: 6.61
Opinions on fringe benefits by gender: 4.156
Prices of laptop computers: 8.113
Property damage in automobile accidents: 4.152
Reducing debt: 11.21
Resale price and age of luxury autos: 3.63
Revenue per kilowatt-hour in Arkansas: 2.47
Salaries of clerk-typists: 8.186
Salaries of elementary school teachers: 2.107
Salaries of human resources clerks: 6.48
Salaries of junior executives: Ex 6.14
Salaries of labor relation managers: 7.38
Salaries of machine shop employees: CPT 2.16
Salaries of registered nurses: 7.42, 7.49
Salaries of resort club managers: 2.39, 2.51
Sales potential ranking and sales totals: CPT 14.13
Savings account amounts: 7.59
Service contractor complaints: AEx 2.17, 2.150
Spa industry profits: AEx 1.2, 1.7
Taxes per capita: 2.81, 2.85
Tax refunds: 1.11
Times to settle insurance claims: 9.103
Total personal income and value of new housing units:
13.39
Total returns in banking industry: 2.24
Turnover among nurse executives: 10.83
Unemployment rates: 3.9, 6.131
Unit pricing: 1.37
Used-car inventory: Ex 4.4
Values of funded projects: 8.15
Waiting time in post office: CPT 8.11, CPT 9.18
Yum Brands abroad: 4.53
College Life
Absences at 8 AM classes: 14.49, 14.72
ACT composite score and first-term college GPA: 13.5
Amount of trash discarded by students: 9.34
Budgeting for intramural and interscholastic sports: 9.73
Caffeine consumption: 9.50
Cars driven by students: Ex 9.8, Ex 9.13, 9.69
Cars owned by college faculty: Ex 1.5
Chemistry students by gender: 9.106
College applications: 5.21
Commute times: CPT 6.15, 9.47
Commute times and distances: 3.22
Commuting distance: 2.141, Ex 8.2, 8.124
Concrete Canoe Competition: 2.66
Cornell’s tuition and ranking: AEx 2.16, 2.149
Cost of textbooks: 1.26, Ex 1.8, 8.180, 9.25, 9.152, 9.153
Course selection criteria: 11.40
Cultural literacy of college freshmen: 12.22
Dropout rate: 6.94
Electronic study guides for accounting principles: 10.63
Final averages: 6.57
Final exam scores by teaching method: CPT 10.14
Genders and majors: Ex 3.1
GPAs and membership in fraternal organizations:
Ex 10.9
Graduation rates: 4.123
Guessing on multiple-choice tests: 5.126
Hours of sleep: 2.70, 2.93, 6.39, 9.54
Hours worked per week: Ex 14.5
Introductory psychology course grades: 11.46
Living at home after graduation: 9.167
Mathematics placement exam scores: 10.50, 10.151
Monthly debt after college graduation: 2.54, 2.168
Number of colleges applied to: AEx 5.3
Number of credit hours: 2.217
Paying off college debt: 2.174
Preference for liberal arts courses by gender: Ex 11.5
Preferences for math course sections: Ex 11.1
Professor late for class: 4.163
Salaries of full professors in Colorado: 14.16
Scholarship applications: 4.118
Self-esteem scores of college students: 10.34, 10.35
Statistics final exam scores: Ex 2.6, Ex 2.12, Ex 2.13,
2.105, Ex 2.19
Statistics pass rates: 4.41
Student characteristics: 1.67
Student credit card debt: 10.1, 10.2, 10.164
Student-owned vehicle makes: 2.8
Students’ places of residence: 11.49
Summer schedule: 1.23, 4.52
Test scores: 9.55
Tuition and fees: 8.42, 10.70
Undergraduate GPA and GPA at graduation: 14.61
Weight of books and supplies: 1.24
Demographics and Population Characteristics
Age and gender of licensed drivers: 4.136
Age at marriage: 7.56
Ages of auto theft offenders: 2.183
Ages of dancers: 2.36
Ages of D.C. residents: 2.9, 4.134
Ages of fishermen: 2.162
Ages of heads of household: 2.220
Ages of licensed drivers: 6.49
Ages of NASCAR drivers: 2.71, 2.94
Ages of New York population: 2.169, 2.176
Ages of night-school students: 8.34
Ages of nuns: 2.42, 2.166
Ages of U.S. population: 2.165, 4.155
Area (sq. mi.) of U.S. states: 2.193
Baby birth days: AEx 11.3, 11.22
Baby birth months: 11.52
Birth weights for babies in U.S.: 8.114
Census data: AEx 1.6, 7.1, 7.2, 7.67, 7.68
College attendance in suburban populations: 2.48
Divorce rates: 1.12
Genders of licensed drivers: 6.95
Grandparents as primary caregivers: 4.117
Gray hair by gender: 10.158
Handedness: 4.66
Height and age of children: 3.17
Height and shoe size: 3.2, 13.72
Height and weight of college women: Ex 3.7, 3.69
Heights and weights of professional soccer team: 3.26
Heights and weights of World Cup players: 3.12, 3.18
Heights of college students: Ex 10.8
Heights of high-school football players: 2.143
Heights of kindergartners: Ex 7.6, Ex 7.7, 7.32, 7.37,
7.43
Heights of male college students: 7.35
Heights of mothers and daughters: 3.11
Heights of NBA players: 2.19, 12.24
Heights of Olympic soccer players: 2.33
Heights of women in health profession: 8.199
High-poverty neighborhood populations: 2.55
Homeownership rates: 11.59
Household incomes: AEx 2.11, 4.11, 14.48
Increases in U.S. population by area: 2.26, 2.142
Life expectancies by gender: 3.95
Monroe Community College demographics: 4.142
Montana’s household population: 2.6
Number of children adopted: 3.44
Number of children fathered by doctors: 2.156
Number of children per family: 5.19
Number of licensed drivers: 1.75, 2.79, 3.24
Number of people per household: 2.34
Number of push-ups and sit-ups: Ex 3.3, Ex 3.5, 3.62
Number of rooms in Texas housing units: 2.35
Number of students by grade level: 1.8
Number of telephones per household: 2.153
Number of televisions in American households: 7.22
Number of televisions in Japanese households: 5.104
Number of years of college of high-tech employees: 8.47
Ophthalmic trait and eye color: 4.154
Percentages in service and trade job categories: 14.63
Political preference by age: 11.61
Poverty and life expectancy: 3.54
Vehicle registrations and population: 3.79
Vehicles per household: 2.80, 4.115, 5.34, 5.106
Weights of adult males: 9.51, 9.52, 11.53
Weights of college students: Ex 2.5
Weights of college women: 8.82, Ex 8.21
Weights of high-school football players: 2.144
Weights of second-grade boys: Ex 8.6
Weights of 10-year-old girls: 8.184
Education and Child Development
ACT exam takers: 2.195
ACT scores: 2.106, 2.126, 2.140, 2.202, 6.52, 6.109
Age at first dental exam: 2.155
AP test results: 2.32, 2.52
Attitudes of preschoolers’ parents: 1.70
Composition exam scores: CPT 9.13
Computer science aptitude test scores: 2.41, 2.53,
10.142, 13.46, 13.50
Content title and reading comprehension: 10.28
Costs of baby supplies: 2.172
Costs of day care: 6.47
Daily activities of schoolchildren: 5.11
Effects of social skills training: 12.61
Equivalence of two exams: Ex 14.6
Evaluation of teaching techniques: AEx 8.11, 8.52, 8.63,
8.64
Examination scores: Ex 2.3, Ex 2.4, 6.117, 14.71
Grade comparison for blondes and brunettes: 10.65
Hours of work per week by high-school juniors and
seniors: 10.66
Hours studied for exam and grade received: 3.15, 3.19,
3.33, 3.38, 3.58, 13.48, 13.51, 13.52
Imaginary friends and coping skills: 9.76
Inherited characteristics of twins: AEx 10.3
Instructional time in social studies: 1.73
International Mathematics and Science Study results for
eighth-graders: 14.17
IQ scores: 6.1, 6.2, Ex 6.10, Ex 6.11, Ex 6.13, 6.45,
6.137, 6.138, 10.133
Irrelevant answers and age: 3.20, 3.39
Kindergarten skills: 1.6
Mastery of basic math by high-school seniors: 14.21
Methods of teaching reading: 12.48
Minimum score required for grade of A: Ex 6.12
Misbehaving and smoking: 5.63
Mothers’ use of personal pronouns when talking with
toddlers: AEx 9.7
National Assessment of Educational Progress in mathematics: 14.65
Number of students per computer in Canada schools:
14.45
Order of finish and scores on exams: Ex 14.14
Parental concerns in choosing a college: 10.100
Physical fitness classes: Ex 10.1
Poverty and proficiency tests: AEx 3.4, 3.16, 3.21, 3.34
Prefinal average and final exam score: 13.84
Proficiency test scores for Ohio fourth-graders: 14.32
Reading proficiency test scores for sixth-graders: 14.7,
14.14
SAT scores: 2.164, CPT 6.16
Social skills in kindergarten: AEx 1.1, AEx 1.9
Standard scores for exam grades: Ex 2.14, 2.122
Strength test scores of third-graders: 2.45, 2.75
Student computer access by grade level: AEx 12.4, 12.9
Summer jobs for high-schoolers: 5.10
TIMSS scores: 7.40, 8.37
Truancy counseling: CPT 10.21
Variability of exam scores: 1.39, 9.176
Wearing of protective clothing by teens: 14.15
Leisure and Popular Culture
Ages of thoroughbred racing fans: 8.151
American Kennel Club registrations by breed: 3.83
Amounts spent on high school prom: 7.41
Aquarium inhabitants: 4.96
Art museum scheduling: 4.165
Asymmetry of euro for coin tossing: AEx 9.14
Blog creators and readers: 11.39
Carnival game probabilities: 4.77, 4.78
Casino gaming rules: AEx 14.12
Cell phone distractions while driving: 1.10
Cell phone text messaging: 9.175
Coffee break: 4.76
Contract bridge hands: 4.45
Cooling mouth after a hot taste: 11.1, 11.2, 11.69
Dimensions and base price of jet boats: 13.57
Dog-obedience training techniques: Ex 14.7
Dog ownership: 4.59, 5.20, 5.36
Downloading music and video files: 6.96
Downloading with cell phones: AEx 11.4, 11.8
Expenditures on leisure activities: 10.60
Halloween candy: 5.80
Help with household chores: 2.13
Hours of housework for men: 7.54
Hours of sleep on weekend: Ex 9.12, 10.128
Hours of television watching: 2.184, 7.23, 14.4
Hours spent housecleaning: AEx 2.7
Impact of Internet on daily life: 5.64
Instant messaging: 6.128
Internet usage: 2.1, 2.2, 2.212, 2.224, 5.79, 9.165
Length of visit to library home page: 8.50
Lengths of pop-music records: 7.62, 7.63
Lottery tickets: 5.113
Lower-leg injuries in skiing: CPT 13.22
M&M colors: 2.197, 4.1, 4.2, 4.3, 4.170, 4.171, 11.57
Misplacements of TV remote control: 2.119
Mother’s Day expenses: 8.117
Number of rolls of film dropped off for developing: 12.32
Number of TV sports reports watched per week: 2.167
Obtaining “comfort food”: 11.54, 11.55, 11.56
Personal watercraft accidents: 9.108
Powerball Lottery game: CPT 4.20
Probability of winning carnival game: Ex 4.13
Rankings of contest participants: Ex 14.13
Rebound heights of table-tennis balls: 14.80
Restaurant wait times: 8.164
Rifle-shooting competition scores: 10.136, 10.141
Shooting accuracy by method of sighting: Ex 12.6
Skittles colors: 11.23, 11.24
Spring cleaning survey: 1.9
Stamp collection value: 8.16
Swimming lessons: 4.10, 4.50, 4.97
Television ratings: 4.29, 4.49
Times for haircuts: 2.206
Time off during holidays: 1.78
Time spent in video games by children: 14.46
Tipping habits of restaurant patrons: 3.66
Use of hair coloring by blondes and brunettes: 10.86
Vacation habits of New York families: 4.141
Vacation research on Internet: 6.130
Valentine’s Day: 2.12, 2.148, 10.129
“Wired” senior citizens: 5.111
Manufacturing and Industry
Absenteeism rates of employees: 11.66
Accuracy of wristwatches: 8.119
Air bag design: Ex 8.8
Amount of force needed to elicit response: 10.163
Amounts of fill: 1.38, 6.53, 6.115, 6.118, 8.194, Ex 9.17,
Ex 10.10, Ex 10.15, Ex 10.17, 10.160, 12.45
Asphalt mixtures: 8.58
Asphalt sampling procedures: AEx 10.7, 10.37
Bad eggs: Ex 5.9
Breaking strength of rope: 8.182
Breaking strengths of steel bars: 7.55
Cellular phone defects: Ex 10.13
Charges for home service call by plumbers: 8.129
Comparing production methods: 10.101, 11.44
Comparing reliability of microcomputers: 10.153
Concrete shrinkage and water content: AEx 3.8
Cork characteristics: AEx 6.15, 8.79, 8.80
Cost per unit and number of units produced per manufacturing run: 3.64
Crew clean-up time: 2.133
Defective bolts: Ex 9.11
Defective parts: 3.85, 4.27, 4.48, 4.67, 4.122, Ex 4.26,
5.67, 9.168, 10.87, 11.37, 14.81
Defective products: 2.15
Defective rifle firing pins: Ex 6.19
Defective television sets: Ex 5.7
Defects in garments: 2.11
Delay times for sprinkler systems: 8.179
Delivery truck capacity: 7.61
Detonating systems for explosives: 8.51, 8.62
Diameter and shear strength of spot weld: 13.58
Diameters of ball bearings: 8.181
Diameters of wine corks: 6.55, 9.60
Drying time for paint: Ex 8.9, Ex 8.14, 8.88, 9.28
Dry weights of corks: 9.141
Effect of heat treatment of length of steel bar: 10.48
Effect of temperature on production level: Ex 12.1, 12.3
Extraction force for wine corks: 6.54, 8.41, 9.182
Failure torque of screws: 9.24
Fill weights of containers: 6.60, 7.36
Flashlight battery lifetimes: CPT6.14, 7.44
Hours worked by production workers: 12.52
Lawn mower warranties: 6.125
Lengths of commutators: 2.21, 9.58
Lengths of lunch breaks: 9.26
Lengths of machined parts: 8.33, 8.39
Lengths of nails: 9.181
Lengths of power door brackets: 2.204
Lengths of wine corks: 9.61
Lens dimensions: 2.72, 6.134, 6.135, 9.150, 10.22, 10.38,
10.74, 10.127, 12.49, 13.60, 13.61, 13.62
Lifetime mileage of tires: 2.132
Lifetimes of cigarette lighters: CPT 7.12
Lifetimes of light bulbs: 2.221, 6.116, 7.57, CPT 8.16,
9.177
Light bulb failures: 5.98
Luxury car colors: 4.56
Machine downtimes: 14.47
Maintenance expenditures for television sets: 9.154
Mileage of automobile tires: 7.58
Mileage of service truck tires: 9.147
Mislabeled shoes: 4.132
Net weights of bags of M&Ms: 6.63
Nutrition information and cost for sports drinks: 3.43,
3.59
Nutrition information for frozen dinners: 8.127
Nutrition information for hot dogs: 2.76
Nutrition information for peanut butter: 12.39
Nutrition information for soups: 2.205, 14.60
Octane ratings of gasoline: 2.182, 9.56
Online queries to PC manufacturers: 11.18
Ovality of wine corks: 8.168
Paint drying time: 2.181
Parachute inspections: 8.56
Particle size of latex paints: 2.203, Ex 8.3, 10.9
Particulate emission in generation of electricity:
CPT 12.14
Performance of detergents: Ex 8.10, Ex 8.12
Product assembly times by gender: 10.159
Proofreading errors: 4.166
Quality control: 1.27, 5.72, 5.119, 7.3
Refrigerator lifetime: 6.114
Rivet strength: 8.81, 8.123
Salvaged tires: 4.151
Screw torque removal measurements: 10.149
Service provided by PC manufacturers: 10.96
Shearing strength of rivets: 6.112, CPT 7.13
Shelf life of photographic chemical: Ex 9.19
Strength and “fineness” of cotton fibers: 13.68
Strength intensity of a signal: 10.135
Sulfur dioxide emissions: Ex 8.19
Temperature of ovens during baking process: 10.119
Tensile strength of cotton fibers: 10.125
Testing rivets: 8.85, 8.128
Test-scoring machine accuracy: 6.124
Thread variance in SUV lug nuts: 10.161
Time for a component to move to next workstation: 8.48
Times for machine adjustments by two methods: 14.78
Toothpaste formulas: 8.86
Toy battery lifetimes: 9.151
Tread wear of tires: 8.190, Ex 10.4, Ex 10.6
T-shirt quality control: 5.47, 5.97, CPT 5.12
Union membership: 4.28, 6.100
Union membership and wages: 4.68
Units of work completed per day: 12.25
Variability of package weights: 9.136
Variability of weightlifting plates: 9.137
Variation in lengths of produced parts: 9.178
Wearing quality of auto tires: Ex 10.2
Weights of bread loaves: 7.34
Weights of cereal boxes: 8.163, 9.183, 9.184, 9.185
Weights of cheese wheels: 10.61
Weights of mini-laptop computers: 8.49
Weights of “1-pound” boxes: 2.161
Weights of packages shipped by air: 8.154
Weights of “10-pound” bags of potatoes: 10.64
Worker satisfaction: 4.131
Marketing and Consumer Behavior
Amount spent by customers: CPT 8.17
Apple-eating preferences: 2.4
Assessing demand for new product: 1.46
Automobile brands of GM employees: 5.50
Baked potato preferences: AEx 11.7, 11.38, 11.45
Blind taste tests for cola preference: 14.19
Bottled water consumption: 6.51
Burger condiments: 9.70
Burger consumption: 9.160
Caffeine consumption: 5.1, 5.2, 5.128, 5.129
Chocolate-covered candy bar preferences: 14.74
Christmas tree sales: 2.194
Coffee drinking trends: 6.129
Coffee preferences of married men: 9.161
Consumer fraud complaints: 5.62
Customer preferences for seating arrangements in
restaurants: CPT 14.19
Deodorant soap preferences: 10.88
Easter candy purchases: 4.124
Effectiveness of different types of advertisements: 12.26
Effectiveness of television commercials: 8.66, 8.67
Effect of sales display location on sales: 12.40
Features desired by home buyers: 14.64
Floor polish preferences: 11.14
Gasoline purchases by method of payment: 3.8
German restaurant ratings: 12.27
Grocery shopping habits: 1.69
Ground beef preferences: 11.17
Holiday shopping preferences: 2.151
“More space” preferences of leisure travelers: 3.3
Movie budgets, box office receipts, and Oscar nominations: 3.46
Nielsen ratings and number of viewers: 3.78
Number of commercials and sales of product: 3.40
Number of customers during noon hour: CPT 2.15
Number of customers per day: 7.53
Number of items purchased: CPT 2.12
Outdoor features desired in new homes: 5.23
Pizza crust preferences: 9.171, 9.172, 9.173, 14.20
Popcorn brand preferences: 11.63
Portuguese wine ratings and prices: 13.23
Price comparisons among grocery stores: 12.41
Product endorsements by athletes: 9.162
Radio hits: 5.112, 11.58
Radio station format preferences over time: 14.86
Ratings and street price ranks of computer monitors:
14.57
Readership of Vogue magazine: 5.108
Restaurant decor rating and cost of dinner: 13.35
Retail store customer data: 12.36, 12.37, 12.38, 12.55,
12.56, 12.57, 13.69, 13.70, 13.71, 13.86, 13.87
Satisfaction with auto service departments: 9.163
Spousal preferences for television programs: 14.84
Television brand ratings: 4.153
Turkey consumption: 7.25
Use of cleaning wipes: 2.10
Medical Science
Abnormal male children and maternal age: 9.157
Acetaminophen content of cold tablets: 9.59
Acute back pain treatments: 10.147
Adverse drug reactions: 9.81, 9.82
Allergies in adults: 1.15
Amount of general anesthetic: 10.137
Amounts of water consumed daily: 8.155, 8.156
Amounts spent on prescription drugs: 9.23
Angina: 10.68
Anticoagulants and bone marrow transplantation: 14.18
Benefits of exercise: 9.1, 9.2, 9.187, 9.188
Blood pressure readings: 10.122
Blood types: 11.48
Body Mass Index (BMI) scores: 8.120, 14.70
Caffeine and dehydration: 9.71
Calculus or tartar: AEx 14.15
Cancer testing: 4.158
Carpal tunnel syndrome: 2.163
Causes of death in United States: 2.175
Cholesterol readings: 10.17, 10.30, 14.34
Clinical trials: 11.43
Clotting time and plasma heparin concentrations:
AEx 13.4
Comparing methods of cataract surgery: 14.33
Crutch length and patient height: 13.63
Dental disease status by height: 4.135
Diabetes by gender: 4.25
Diastolic blood pressure readings: 10.47
Effect of calcium channel blockers on pulse rate: Ex 10.5
Effect of diet on uric acid level: 10.8
Effect of drug in lowering heart rate: 13.67
Effects of biofeedback and relaxation on blood pressure:
12.23
Exercise capacity of police recruits: 2.97
Eye-nose-throat irritations: 11.36
Fertility rate: 7.24
Flu vaccine: 1.71
Graft-versus-host disease in patients with acute myeloid
leukemia: 14.13
Handedness and death rates from accident-related injuries: 10.156
Health benefits of exercise: 1.45
Health status of older Americans: 1.79
Hemoglobin test for diabetic patients: 2.44
Hip-replacement surgery: 5.105
Hospital stays after surgery: 12.21
Hypertension: 1.25
Immediate-release vs. sustained-release codeine: 10.138
Infant mortality rates: 2.108, 6.133
Injury severity in younger and older children: 10.120
Length of pain relief: 12.42
Life expectancy: 1.80
Lung cancer and smoking: 4.26
Lung cancer survival rate: 9.90
Manual dexterity scores: 2.110
Marriage and health status: 1.74
Maternal death rates: 4.46
Medical assistance for accident victims: 8.57
Melanoma survival rates: 6.93
Methods for teaching anatomy: AEx 10.11, 10.67, 14.77
Mineral concentration in tissue samples: 14.59
Noise level in hospitals: CPT 8.18
Organ donation: 11.65
Percentages of nicotine in cigarettes: 14.30
“Persistent disagreements” in therapeutic recreation:
2.118
Plasma concentration of ranitidine: 13.78
Plasma protein binding of diazepam: 12.60
Prescription drug use: 1.81
Prescription drug use by seniors: 9.170
Pulse rates: 9.29, 9.30, 14.31
Response time to blood pressure medication: 8.171
Salt-free diets and diastolic blood pressure: 10.19
Self-care test scores of recently diagnosed diabetics:
10.29
Side effects of drugs: 1.22, 1.29, 5.107, 10.102
Sleep apnea: 4.60
Substance abuse: 1.82, 6.99
Surgical infections: AEx 1.7
Survival rate during surgery: 5.66
Testing effectiveness of new drugs: 8.195, 8.196
Time since last doctor visit by age: 3.84
Types of operations: Ex 2.1
Use of electrical stimulation to increase muscular
strength: 13.79
Use of nuclear magnetic resonance spectroscopy for detection of malignancy: 14.77
Vertigo treatments: 12.31
Wait time for urgent care: 9.146
Weight loss on no-exercise plan: Ex 14.3
Weights before and after smoking cessation: CPT 10.15,
CPT 14.11
Weights of newborns: Ex 9.4
Physical Sciences
Accuracy of short-range missiles: CPT 10.17
Amount of rainfall for April: AEx 12.5, 12.10
Area and maximum depth of world lakes: 3.97
Atmospheric ammonium ions: 2.112
Atomic weight of silver: 8.40
Carbon monoxide readings in Rochester: Ex 8.13, Ex 9.5
Density of nitrogen: 2.188
Density of the earth: 2.118, 9.57
Duration and path width of solar eclipses: 3.28
Durations of eruptions of Old Faithful: 2.46
Effects of cloud seeding on rainfall amounts: 14.35
Elevations of towns in upstate New York: 2.96
Forecasting hurricanes: 5.33
Hailstone size and wind updraft speed: 13.42
Heating-degree-day data: 2.28, 2.95
High temperatures: 5.8, Ex 14.1, Ex 14.4, 14.5
Hydrogen characteristics in seasonal snow packs: 14.69
Lightning strikes: 2.38
Number of sit-ups in 1 minute: 10.36
Old Faithful eruption data: 3.102
Parallax of the sun: 9.32
Precipitation in New York State: 6.110
Prediction of next eruption of Old Faithful: AEx 8.1, 8.17
Pressure and total aluminum content for Horn blende
rims: 13.80
Roughness coefficient for quartz sand grains: 14.75
Target error of short-range rockets: 10.148
Test flow rates in dual bell rockets: 10.46
Velocity of light: 9.159, 12.34
Water content of snow: AEx 8.5, 8.43
Water pollution readings: 9.156
Weather forecasts: 4.13
Wind speeds in Honolulu: 7.39
Psychology, Sociology, and Social Issues
Achievement test scores of soldiers: 10.140
Affirmative Action Program for federal contractors:
AEx 5.10
African-American roles in cinema releases: 11.16
Ages of antitrust offenders: 9.22
Amount that requires consultation with spouse before
spending: 8.38
Anxiety test scores: 10.139
Attitudes toward death: 10.44
Bikers and body art: 5.68
Destruction-of-property offenses among school-age boys
and girls: CPT 10.16
Determining the “goodness” of a test question: 10.154
Driving while drowsy: 5.81
Drug addiction: 5.74
Earphone use on flights: 5.91
Effect of suburb position on school population: 12.30
Establishing the reliability of a test: 13.21
Family structure: Ex 4.3, 4.168, 5.6, 5.69
Fear of darkness: 11.41
Fear of dentist by age: 3.81
Fear of public speaking: 9.109
Hate crimes: Ex 2.2
Households with guns: 11.25
Ideal age: 3.5, 12.33
Ideal age to live forever: 5.12
Images of political candidates: 10.97
Job satisfaction: Ex 8.15, Ex 8.20
Job satisfaction of nurses in magnet and non-magnet
hospitals: 11.19
Job satisfaction rankings by workers and boss: 14.56
Legalization of marijuana for medical purposes: 9.107
Lifetime learning activities: 5.114
Marriage proposals by women: 10.103
Memory test scores: 10.16, 10.150
Methods of disciplining children: 6.126
Personality characteristics of police academy applicants:
AEx 10.20, 10.124
Proportions of Catholic and non-Catholic families in private schools: CPT 10.22
Psychology experiment: 10.7
Reporting cheating on exam: 5.109
Self-image test scores of public-assistance recipients:
Ex 9.6
Sizes of communities reared in and residing in: 11.33
Teenagers’ views on contemporary issues: 14.1, 14.2,
14.89
Teen gambling: 9.74, 10.85
Television news preference and political affiliation: 3.7
Testing prospective employees: Ex 8.16
Test scores of clerk-typist applicants: 8.165
Volunteer work by children: 9.104
Worker opinions on biometric technology: 5.92
Worker-supervisor relationships: 11.35
Public Health and Safety
Ages of volunteer ambulance members in upstate New
York: 8.161
AIDS knowledge test scores: 10.146
Air pollution rankings of U.S. cities: 14.58
Arrests for drug law violations: 12.50
Bike helmet laws: 9.86
Distance to nearest fire department: 8.152
“Five-second rule” for food safety: 2.171
Hand washing in public restrooms: 4.99
Helmet use with wheeled sports: 1.77
Medically Needy Program in Oregon: 5.22
Number of engines owned by fire departments: 8.6
Number of reported crimes by district: 11.60
Opinions on police agency organization by residence:
Ex 4.24
Police officer exams: CPT 4.16
Population and violent crime rate: 13.37
Quality of service station restrooms: 11.34
Scores on Emergency Medical Services Certification
Examination: 8.149
Seat belt usage: 9.89, 11.32
Seriousness weights in index of crime: AEx 13.7, 13.49
Speed limits—85th percentile rule: AEx 2.15
Tobacco settlement and population: 13.82
Traffic ticket and accident probability: 4.100
Weapons in school: 11.42
Sports
Archery: 5.9
Attempted passes by NFL quarterbacks: 2.208
Baseball batting average: 5.71
Comparison of college football poll rankings: 14.87
Distance to centerfield fence in MLB stadiums: 2.116
Distribution of gold, silver, and bronze medals at
Olympics: 13.76
Durability of golf balls: 12.51
Duration of MLB games: 6.113, 8.153, 8.167, 10.72
Earnings of Nationwide Tour professional golfers: 2.189
Football players’ sprint times on artificial turf and grass:
10.145
Football’s winning coaches: 4.14
Graduation rates of NCAA tournament teams: 2.113
High school basketball: 2.17
High school basketball injuries: 4.98, 11.64
Home runs in MLB: 1.76, 2.20
MLB runs scored at home and away: 2.77, 3.93
MLB team batting averages and earned run averages by
league: 14.79
MLB won/loss percentages for away games by division:
12.29
Most holes played by golfers: 11.51
NBA coach records: 6.97
NBA players in Olympics: 13.38
NBA players” points scored and personal fouls committed per game: 3.1, 3.48, 3.105
NBA playoffs: 5.83
NCAA basketball: 4.44
Number of golf tournaments played by professionals:
2.170
Number of wins and earned run averages in MLB: 3.73
Odds against making professional sports team: AEx 4.7
Olympic biathlon: 5.65
Performance of Olympic gold medal winners over time:
3.25
PGA top money leaders and world rankings: 3.76
PGA tournament scores: 2.37
Points earned by NASCAR drivers: 2.207
Points per game and All-Star appearances of NBA players: 13.43
Points scored by NBA teams: 2.7
Points scored for and against NFL teams: 12.47, 13.11
Running times on cinder tracks and synthetic tracks:
14.73
“Size” measurements for MLB stadiums: 3.23
Soccer goals: 2.31
Sports championship series: 4.167
Steroid testing for athletes: 4.73, 4.116, 5.116
Stride rate and speed of serious runners: 3.68
Success rates for PGA players from various distances
from the greens: 3.71
Super Bowl odds: 4.43
Surveys and Opinion Polls
Attitudes of men and women on managing stress:
10.155
Cluster sampling: 1.56
Election poll: 1.68, Ex 4.8, Ex 4.9, Ex 4.14, Ex 4.15,
Ex 4.20
Female president of United States: 6.98
Grid sampling: 1.49
Managers and professionals working late: 9.75
Margins of error in nationwide polls: AEx 9.9, 9.79
Opinions on budget proposal: Ex 4.11, Ex 4.12, Ex 4.19
Opinions on executive compensation: 10.99
Political election: 8.68, Ex 10.12
Poll on proposed legislation: Ex 11.4
Poll on recycling: CPT 11.18
Random sampling: 1.50, 1.51
Refusing job offer because of family considerations:
10.98
Research Randomizer: 14.52
Sample size for customer survey: 9.166
Sampling frame: 1.48, 1.57
Sampling methods: 1.41
Sampling student bodies at two schools: 7.26
“Sexiest job” poll: 6.127
Support for “get tough” policy in South America: 10.152
Systematic sample: 1.53
Telephone surveys: 1.52
Transportation
Ages of urban transit rail vehicles: AEx 7.3
Airline complaints: 2.14, 2.187, 3.77, 4.12, 11.62
Airline engine reliability: 5.110
Airline on-time rates: 2.73, 2.99, 2.115, 6.132, 14.62
Airport runways: 4.51
Automobile speeds on expressway: 6.58
Baggage weights of airline passengers: 7.60
Bicycle fatalities and injuries: 4.54
Bridge conditions in North Carolina: 5.120
Car rental rates: 10.45, 14.8
Death rates on rural roads: 13.24
Distance between interchanges on interstates: 2.61
Fuel economy of SUVs: 9.33
Mass transit system data for large cities: 3.100
Maximum speed limits on interstate highways: 3.6
Miles per gallon of gasoline: 3.87, Ex 8.18, 8.172, 9.140
Motor-fuel consumption: 2.78
Number of miles of interstate highways: 2.60, 2.192,
3.45, 3.47, 3.74
On-time commutes: 4.74
Railroad riders: 4.9
Railroad violations: 4.133
Ship arrivals in harbor: 5.35, 5.103
Space shuttle reliability: 4.114
Speed of Eurostar train: 8.36
Speeds of automobiles: 2.43
Stopping distance on wet surface: 2.185, Ex 3.2, 12.43
Structurally deficient bridges: 2.98, 2.125
Taxi fares: 8.5
Thunderstorms and on-time flights: 4.150
Traffic circles: 4.148
Traffic control: 4.30, 4.137
Traffic fatalities: 2.114, 4.4
Transportation in D.C.: 4.55
Travel time index: 9.186
Wait times in airport security lines: 5.24
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Elementary Statistics
TENTH EDITION
Robert Johnson
Patricia Kuby
Monroe Community College
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Elementary Statistics Enhanced Review Edition, Tenth Edition
Robert Johnson and Patricia Kuby
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Brief Contents
CHAPTER 1
Statistics 1
CHAPTER 2
Descriptive Analysis and Presentation of
Single-Variable Data 38
CHAPTER 3
Descriptive Analysis and Presentation of Bivariate Data 144
CHAPTER 4
Probability 204
CHAPTER 5
Probability Distributions (Discrete Variables) 268
CHAPTER 6
Normal Probability Distributions 312
CHAPTER 7
Sample Variability 360
CHAPTER 8
Introduction to Statistical Inferences 394
CHAPTER 9
Inferences Involving One Population 472
CHAPTER 10
Inferences Involving Two Populations 544
CHAPTER 11
Applications of Chi-Square 618
CHAPTER 12
Analysis of Variance 656
CHAPTER 13
Linear Correlation and Regression Analysis 694
CHAPTER 14
Elements of Nonparametric Statistics 748
iii
This page intentionally left blank
Detailed Contents
PART 1
Descriptive Statistics
Chapter 1
Statistics 1
1.1
1.2
1.3
1.4
1.5
1.6
Chapter 2
Descriptive Analysis and Presentation of Single-Variable Data 38
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
Chapter 3
Chapter 4
You and the Internet 39
Graphs, Pareto Diagrams, and Stem-and-Leaf Displays 40
Frequency Distributions and Histograms 55
Measures of Central Tendency 73
Measures of Dispersion 84
Measures of Position 92
Interpreting and Understanding Standard Deviation 106
The Art of Statistical Deception 114
Mean and Standard Deviation of Frequency Distribution (optional) 117
Descriptive Analysis and Presentation of Bivariate Data 144
3.1
3.2
3.3
3.4
PART 2
Americans, Here’s Looking at You 1
What Is Statistics? 3
Measurability and Variability 17
Data Collection 18
Comparison of Probability and Statistics 27
Statistics and Technology 28
The Kid Is All Grown Up 145
Bivariate Data 146
Linear Correlation 162
Linear Regression 173
Probability
Probability 204
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Sweet Statistics 205
Probability of Events 207
Conditional Probability of Events 223
Rules of Probability 228
Mutually Exclusive Events 236
Independent Events 243
Are Mutual Exclusiveness and Independence Related? 249
v
vi
DETAILED CONTENTS
Chapter 5
Probability Distributions (Discrete Variables) 268
5.1
5.2
5.3
5.4
5.5
5.6
Chapter 6
Normal Probability Distributions 312
6.1
6.2
6.3
6.4
6.5
6.6
Chapter 7
Caffeine Drinking 269
Random Variables 270
Probability Distributions of a Discrete Random Variable 273
Mean and Variance of a Discrete Probability Distribution 278
The Binomial Probability Distribution 284
Mean and Standard Deviation of the Binomial Distribution 300
Intelligence Scores 313
Normal Probability Distributions 315
The Standard Normal Distribution 316
Applications of Normal Distributions 323
Notation 338
Normal Approximation of the Binomial 343
Sample Variability 360
7.1
7.2
7.3
7.4
275 Million Americans 361
Sampling Distributions 363
The Sampling Distribution of Sample Means 369
Application of the Sampling Distribution of Sample Means 377
PART 3
Inferential Statistics
Chapter 8
Introduction to Statistical Inferences 394
8.1
8.2
8.3
8.4
8.5
8.6
Chapter 9
Inferences Involving One Population 472
9.1
9.2
9.3
9.4
Chapter 10
Were They Shorter Back Then? 395
The Nature of Estimation 397
Estimation of Mean μ (σ Known) 402
The Nature of Hypothesis Testing 416
Hypothesis Test of Mean μ (σ Known): A Probability-Value Approach 426
Hypothesis Test of Mean μ (σ Known): A Classical Approach 444
Get Enough Daily Exercise? 473
Inferences About Mean μ (σ Known) 474
Inferences About the Binomial Probability of Success 496
Inferences About the Variance and Standard Deviation 516
Inferences Involving Two Populations 544
10.1
10.2
10.3
10.4
Students, Credit Cards, and Debt 545
Dependent and Independent Samples 547
Inferences Concerning the Mean Difference Using Two
Dependent Samples 550
Inferences Concerning the Difference Between Means Using Two
Independent Samples 564
DETAILED CONTENTS
10.5
10.6
Inferences Concerning the Difference Between Proportions Using Two
Independent Samples 581
Inferences Concerning the Ratio of Variances Using Two
Independent Samples 592
PART 4
More Inferential Statistics
Chapter 11
Applications of Chi-Square 618
11.1
11.2
11.3
11.4
Chapter 12
Time Spent Commuting to Work 657
Introduction to the Analysis of Variance Technique
The Logic Behind ANOVA 666
Applications of Single-Factor ANOVA 670
658
Linear Correlation and Regression Analysis 694
13.1
13.2
13.3
13.4
13.5
13.6
13.7
Chapter 14
Cooling a Great Hot Taste 619
Chi-Square Statistic 620
Inferences Concerning Multinomial Experiments 622
Inferences Concerning Contingency Tables 633
Analysis of Variance 656
12.1
12.2
12.3
12.4
Chapter 13
vii
Wheat! Beautiful Golden Wheat! 695
Linear Correlation Analysis 697
Inferences about the Linear Correlation Coefficient 703
Linear Regression Analysis 712
Inferences Concerning the Slope of the Regression Line 718
Confidence Interval for Regression 727
Understanding the Relationship between Correlation and Regression 737
Elements of Nonparametric Statistics 748
14.1
14.2
14.3
14.4
14.5
14.6
14.7
Teenagers’ Attitudes 749
Nonparametric Statistics 750
Comparing Statistical Tests 751
The Sign Test 752
The Mann-Whitney U Test 765
The Runs Test 776
Rank Correlation 785
Appendix A: Basic Principles of Counting 804
Appendix B: Tables 805
Answers to Selected Exercises 829
Answers to Chapter Practice Tests 872
Index 879
Introductory Concepts and Review Lessons with Answers 885
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Preface
Our Approach
Over the years, Elementary Statistics has developed into a readable introductory
textbook that promotes learning, understanding, and motivation by presenting
statistics in a real-world context for students without sacrificing mathematical
rigor. In addition, Elementary Statistics has responded to the gradual acceptance by
almost every discipline that statistics is a most valuable tool for them. As a result, the applications, examples, projects, and exercises contain data from a wide
variety of areas of interest, including the physical and social sciences, public
opinion and political science, business, economics, and medicine.
Now, more than 30 years after Elementary Statistics was first published, at least
one statistics course is recommended for students in all disciplines, because statistics today is seen as reaching into multiple areas of daily life. Despite this
change in perception, our approach has not changed. We continue to strive for
readability and a common-sense tone that will appeal to students who are increasingly more interested in application than in theory.
Coverage in the New Edition
NEW Chapter 1—Statistics: This chapter has been rewritten to place a
greater emphasis on interpretation of statistical information when learning key
statistical terms and procedures.
Chapter 3—Descriptive Analysis and Presentation of Bivariate Data: Descriptive regression and correlation are introduced early in the presentation
for those who prefer this approach. Continuing with relationships between two
variables makes for a logical progression of material and satisfies students’ natural curiosity about two variables after studying descriptive statistics of one variable. In addition, this early introduction allows instructors to go through nearly
all of the thought process for a hypothesis test without any of the technical
names and procedures. Later, in Chapter 8, when it comes time to introduce the
hypothesis test procedure, by reusing the correlation decision as an introductory
example, students will feel comfortable with the “new” testing process.
NEW Chapter 4—Probability: This chapter has been completely revised
with increased focus on analysis as opposed to formulas to increase student interest and comprehension of this sometimes challenging topic.
p-Value and classical approaches to hypothesis testing are introduced separately, but are thereafter presented side-by-side to offer pedagogical flexibility
and to emphasize their comparability.
ix
x
PREFACE
Tour of the New Edition
Gain a better understanding of algebraic
and basic statistical concepts with author
Patricia Kuby’s Introductory Concepts and
Review Lessons with Answers now included
with this text. Explanations of topics are
presented so that one can learn the fine
details without getting lost in the statistical
involvement, and once the basic concepts
are mastered, the step to incorporating
them into statistics will be natural and
fluid. Additional practice is provided to
ensure understanding.
CHAPTER
8
Chapter Outlines
appear at the beginning of each chapter to
give an overview of what is to be presented.
Introduction
to Statistical
Inferences
8.1
Were They Shorter Back Then?
8.2
The Nature of Estimation
8.3
Estimation of Mean ( known)
8.4
The Nature of Hypothesis Testing
8.5
Hypothesis Test of Mean ( known): A Probability-Value
Approach
8.6
Hypothesis Test of Mean ( known): A Classical Approach
© Christa Renee/Getty Images
NEW and Updated
Chapter Opening
Sections serve as an “example
introduction,” demonstrating statistics
in action with respect to the specific
chapter’s material. Each example
illustrates a familiar situation using
statistics in a relevant, approachable
manner for the student.
8.1
Throughout the chapter, this icon
introduces a list of resources on the
StatisticsNow website at
that will:
• Help you evaluate your
knowledge of the material
• Allow you to take an
exam-prep quiz
• Provide a Personalized learning
Plan targeting resources that
address areas you should study
Were They Shorter Back Then?
WERE THEY SHORTER BACK THEN?
The average height for an early 17thcentury English man was approximately
5' 6''. For 17th-century English women, it
was about 5' 1/2''. While average heights in
England remained virtually unchanged in
the 17th and 18th centuries, American
colonists grew taller. Averages for modern
Americans are just over 5' 9'' for men, and
about 5' 3 3/4'' for women. The main reasons for this difference are improved nutrition, notably increased consumption of
meat and milk, and antibiotics.
Source: />
The National Center for Health Statistics (NCHS) provides statistical information that guides actions and policies to improve the health of the American
people. Recent data from NCHS give the average height of females in the
United States to be 63.7 inches, with a standard deviation of 2.75 inches.
PREFACE
Chapter Project
NEW and Updated
Chapter Projects, at the
end of each chapter,
bring the Chapter
Opening Sections full
circle by incorporating
the chapter’s material.
A complete mini-study
is also provided for
individual student or
small group investigations.
Were They Shorter Back Then?
Data from the National Center for Health Statistics
indicate that the average height of a female in the
United States is 63.7 inches with a standard deviation of 2.75 inches. Use the data on heights of females in the health profession from Section 8.1,
“Were They Shorter Back Then?” (p. 395), to answer the following questions. [EX08-001]
65.0
63.0
70.0
64.5
64.0
66.0
62.0
63.0
69.0
66.0
64.0
63.0
63.0
63.5
65.0
67.0
64.0
68.0
69.0
69.0
59.0
72.0
58.0
62.0
67.0
69.0
66.0
60.0
58.0
66.5
66.0
65.0
63.5
66.0
67.5
69.0
64.0
66.0
68.0
62.0
64.0
67.0
64.0
59.0
70.0
d. On the same histogram used in part b of
Exercise 8.1 on page 396:
61.5
68.0
62.0
56.0
62.0
e.
Putting Chapter 8 to Work
8.199 a. Are the assumptions of the confidence
interval and hypothesis test methods of
this chapter satisfied? Explain.
b. Using the sample data and a 95% level
of confidence, estimate the mean
height of females in the health profession. Use the given population standard
deviation of 2.75 inches.
Updated
Plentiful Examples,
throughout the text,
present the step-by-step
solution process for
key statistical concepts
and methods.
c. Test the claim that the mean height of
females in the health profession is different from 63.7 inches, the mean
height for all females in the United
States. Use a 0.05 level of significance.
318
CHAPTER 6
EXAM PLE 6.2
(i)
Draw a vertical line at the hypothesized population mean value, 63.7.
(ii)
Draw a horizontal line segment
showing the 95% confidence interval found in part b.
Does the mean ϭ 63.7 fall in the interval? Explain what this means.
f. Describe the relationship between the
two lines drawn on your graph for part c
of Exercise 8.2 on page 396 and the two
lines drawn for part d of this exercise.
g. On the basis of the results obtained earlier, does it appear that the females in
this study, on average, are the same
height as all females in the United States
as reported by the NCHS? Explain.
Normal Probability Distributions
Finding Area in the Right Tail of a Normal Curve
Find the area under the normal curve to the right of z ϭ 1.52: P(z Ͼ 1.52).
S O L U T I O N The area to the right of the
mean (all the shading in the figure) is exactly 0.5000. The problem asks for the
shaded area that is not included in the
0.4357. Therefore, we subtract 0.4357
from 0.5000:
Area in table
Area asked for
0.4357
z = 0 z = 1.52
z
P(z Ͼ 1.52) ϭ 0.5000 Ϫ0.4357 ϭ 0.0643
Note: As we have done here, always draw and label a sketch. It is most helpful.
Make it a habit to write z with two decimal places and areas and probabilities with four decimal places, as done in Table 3.
Updated
Relevant Applied
Examples incorporate
statistical concepts to
demonstrate how
statistics work in the
real world.
APPLI E D
EXAM PLE 1.1
Telling Us about Our Early Behavior
Remember going to kindergarten? EVEN IN KINDERGARTEN, SOCIAL SKILLS TRUMP
Percentage of 800 kingergarten teachers surveyed
Maybe, maybe not! If you do rewho say these skills are essential or very important:
member, your first concern was
100%
most likely whether you would
have a good time and make some
friends. What would your teacher’s
concerns have been?
Consider the information included in the graphic “Even in
kindergarten, social skills trump.”
It describes the skills that kindergarten teachers consider essential
0%
or very important. Eight hundred
Paying Not being Following Getting Problem- Knowing Counting
attention disruptive directions along
to 20
solving
the
kindergarten teachers (only a frac86%
86%
83% with others 61% alphabet 27%
tion of all of them) were surveyed,
83%
32%
producing the skills and percent- Data from Julia Neyman and Alejandro Gonzalez, © 2004 USA Today.
ages reported. Leading the list are
“Paying attention” and “Not being disruptive.” Of the 800 surveyed teachers,
86% considered these skills essential or very important. Looking at all the per-
xi
xii
PREFACE
NEW Did You Know?
short history stories
and fun facts provide
an informative and
entertaining look at
related concepts or
methods being presented
in the corresponding
section.
The standard normal variable z is our test statistic for this hypothesis test.
DID YOU KNOW
Disputes in Approach
Statistics is not just mathematics. There are different
ways to approach statistical inferences and different ways to
interpret what the data are
telling. The more significant
the differences, the more likely
there are to be heated disagreements between those of
opposing viewpoints. Just such
a dispute erupted in 1935 at a
Royal Statistical Society discussion when R. A. Fisher
challenged Jerzy Neyman with
regard to his being fully acquainted with the topic being
discussed. The dispute centered on Pearson and
Neyman’s use of confidence
intervals and approach to hypothesis testing versus Fisher’s
intervals and concept of pvalues in significance testing.
The feud lasted until Fisher’s
death in 1962.
Critical region: The set of values for the test statistic that will cause us to reject
the null hypothesis. The set of values that are not in the critical region is called the
noncritical region (sometimes called the acceptance region).
Recall that we are working under the assumption that the null hypothesis
is true. Thus, we are assuming that the mean shearing strength of all rivets in
the sampled population is 925. If this is the case, then when we select a random sample of 50 rivets, we can expect this sample mean, xෆ, to be part of a
normal distribution that is centered at 925 and to have a standard error of
/͙n
ෆ ϭ 18/͙50
ෆ, or approximately 2.55. Approximately 95% of the sample
mean values will be greater than 920.8 (a value 1.65 standard errors below the
mean: 925 Ϫ (1.65)(2.55) ϭ 920.8). Thus, if Ho is true and ϭ 925, then we
expect xෆ to be greater than 920.8 approximately 95% of the time and less than
920.8 only 5% of the time.
x Ͻ 920.8 x greater than 920.8
5%
95%
920.8
x
925
If, however, the value of ෆx that we obtain from our sample is less than
920.8—say, 919.5—we will have to make a choice. It could be that either: (A)
such an xෆ value (919.5) is a member of the sampling distribution with mean
925 although it has a very low probability of occurrence (less than 0.05), or (B)
ෆx ϭ 919.5 is a member of a sampling distribution whose mean is less than 925,
which would make it a value that is more likely to occur.
Any distribution
with Ͻ 925
0.05
920.8
x
925
919.5
NEW and Updated
With nearly 550 new
exercises and almost
100 updated exercises,
the new edition of
Elementary Statistics
provides instructors with
up-to-date, relevant
homework sets geared
toward students’
interests.
NEW and Updated
More than 300 classic
Exercises are also
available on the
Student’s Suite CD-ROM,
as well as the solutions to
odd-numbered exercises.
SECTION 8.3 EXE RCISES
Skillbuilder Applet Exercises must be worked using an
accompanying applet found on your Student’s Suite CD-ROM or at
the StatisticsNow website at .
Datasets can be found on your Student’s Suite CD-ROM or at the
StatisticsNow website at .
8.19 Discuss the conditions that must exist before
we can estimate the population mean using the interval techniques of formula (8.1).
8.23 Given the information, the sampled population is normally distributed, n ϭ 16, ෆx ϭ 28.7, and
ϭ 6:
a. Find the 0.95 confidence interval for .
b. Are the assumptions satisfied? Explain.
8.24 Given the information, the sampled population is normally distributed, n ϭ 55, ෆx ϭ 78.2, and
ϭ 12:
a. Find the 0.98 confidence interval for .
b. Are the assumptions satisfied? Explain.
8.20 Determine the value of the confidence coefficient z(␣/2) for each situation described:
a. 1 Ϫ ␣ ϭ 0.90
b. 1 Ϫ ␣ ϭ 0.95
8.25 Given the information, n ϭ 86, ෆx ϭ 128.5,
and ϭ 16.4:
a. Find the 0.90 confidence interval for .
8.21 Determine the value of the confidence coefficient z(␣/2) for each situation described:
b. Are the assumptions satisfied? Explain.
a. 98% confidence
8.26 Given the information, n ϭ 22, ෆx ϭ 72.3, and
ϭ 6 4:
b. 99% confidence
Chapter Exercises
6.102 The middle 60% of a normally distributed
population lies between what two standard scores?
Go to the StatisticsNow website to
With more than 2100
exercises, students will
have ample opportunity
for practice and instructors will have a greater
choice of exercises to
use in their course.
• Assess your understanding of this chapter
• Check your readiness for an exam by taking the Pre-Test quiz
and exploring the resources in the Personalized Learning Plan
Datasets can be found on your Student’s Suite CD-ROM or at the
StatisticsNow website at .
6.101 According to Chebyshev’s theorem, at least
how much area is there under the standard normal
distribution between z ϭ Ϫ2 and z ϭ ϩ2? What is
the actual area under the standard normal distribution between z ϭ Ϫ2 and z ϭ ϩ2?
6.103 Find the standard score (z) such that the
area above the mean and below z under the normal curve is:
a. 0.3962
b.
0.4846
c.
0.3712
6.104 Find the standard score (z) such that the
area below the mean and above z under the normal curve is:
a. 0.3212
b.
0.4788
c.
0.2700
PREFACE
Updated Skillbuilder
Applet Exercises, found
in Section and Chapter
Exercises, help students
“see” statistical concepts
and allow hands-on
exploration of statistical
concepts and calculations.
To explore the
accompanying applets,
students can find them
on the Student’s Suite
CD-ROM or in
StatisticsNow.
xiii
SECTION 6.4 EXE RCISES
6.41 Given x ϭ 58, ϭ 43, and ϭ 5.2, find z.
Skillbuilder Applet Exercises must be worked using an
accompanying applet found on your Student’s Suite CD-ROM or at
the StatisticsNow website at .
Datasets can be found on your Student’s Suite CD-ROM or at the
StatisticsNow website at .
6.39 Skillbuilder
Applet
Exercise demonstrates that
probability is equal to the
area under a curve. Given
that college students sleep
an average of 7 hours per
night with a standard deviation equal to 1.7 hours,
use the scroll bar in the applet to find the
following:
a. P(a student sleeps between 5 and 9 hours)
b. P(a student sleeps less than 4 hours)
6.42 Given x ϭ 237, ϭ 220, and ϭ 12.3, find z.
6.43 Given that x is a normally distributed random
variable with a mean of 60 and a standard deviation of 10, find the following probabilities:
a.
P (x Ͼ 60)
d.
P (65 Ͻ x Ͻ 82) e. P (38 Ͻ x Ͻ 78) f.
b.
P (60 Ͻ x Ͻ 72) c.
P (57 Ͻ x Ͻ 83)
P (x Ͻ 38)
6.44 Given that x is a normally distributed random
variable with a mean of 28 and a standard deviation of 7, find the following probabilities:
a.
P (x Ͻ 28)
d.
P (30 Ͻ x Ͻ 45) e. P (19 Ͻ x Ͻ 35) f.
b.
P (28 Ͻ x Ͻ 38) c.
P (24 Ͻ x Ͻ 40)
P (x Ͻ 48)
6.45 Using the information given in Example 6.10
(p. 324):
a
Find the probability that a randomly selected
New and Updated Expanded Chapter Review, tailored to reviewers’ feedback
and students’ needs, functions as a chapter study guide at the end of each chapter. Each Chapter Review includes:
•
In Retrospect, a summary of concepts learned in each chapter that points
out the relationships between previously covered material.
In Retrospect
We have learned about the standard normal probability distribution, the most important family of
continuous random variables. We have learned to
apply it to all other normal probability distributions and how to use it to estimate probabilities of
binomial distributions. We have seen a wide vari-
•
ety of variables that have this normal distribution
or are reasonably well approximated by it.
In the next chapter we will examine sampling
distributions and learn how to use the standard
normal probability to solve additional applications.
Vocabulary and Key Concept List, which give students an idea of how
much of the material they truly understand.
Vocabulary and Key Concepts
area representation for probability (p. 316)
bell-shaped curve (p. 315)
binomial distribution (p. 343)
binomial probability (p. 343)
continuity correction factor
( 344)
•
continuous random variable
(pp. 315, 344)
discrete random variable
(pp. 315, 344)
normal approximation of binomial (p. 343)
l
( 316)
percentage (p. 316)
probability (p. 316)
proportion (p. 316)
random variable (p. 315)
standard normal distribution
(pp. 316, 323, 338)
t d d
(
316 323)
Learning Outcomes, a summary list outlining the key concepts that should
have been learned through the course of the chapter accompanied by corresponding review exercises and section references to ensure comprehension
of the chapter material.
Learning Outcomes
✓ Understand the difference between a discrete and continuous random
variable.
p. 315
✓ Understand the relationship between the empirical rule and the
normal curve.
pp. 313–314, Ex. 6.1
✓ Understand that a normal curve is a bell-shaped curve, with total
area under the curve equal to 1.
pp. 315–316, EXP 6.1,
Ex. 6.40
✓ Understand that the normal curve is symmetrical about the mean,
pp. 315–317, EXP. 6.2
xiv
PREFACE
•
Chapter Exercises, which offer practice on all the concepts found in the
chapter while also tying in comprehensive material learned from previous
chapters.
binomial.
6.129
Chapter Exercises
6.102 The middle 60% of a normally distributed
population lies between what two standard scores?
Go to the StatisticsNow website to
• Assess your understanding of this chapter
• Check your readiness for an exam by taking the Pre-Test quiz
and exploring the resources in the Personalized Learning Plan
Datasets can be found on your Student’s Suite CD-ROM or at the
StatisticsNow website at .
6.101 According to Chebyshev’s theorem, at least
how much area is there under the standard normal
distribution between z ϭ Ϫ2 and z ϭ ϩ2? What is
the actual area under the standard normal distribution between z ϭ Ϫ2 and z ϭ ϩ2?
•
6.103 Find the standard score (z) such that the
area above the mean and below z under the normal curve is:
a. 0.3962
b.
0.4846
c.
0.3712
6.104 Find the standard score (z) such that the
area below the mean and above z under the normal curve is:
a. 0.3212
b.
0.4788
c.
0.2700
Chapter Project, which offers students the opportunity to revisit the Chapter Opening Sections to answer the questions proposed at the beginning of
the chapter, using the knowledge gained from studying the chapter.
Chapter Project
Intelligence Scores
All normal probability distributions have the same
shape and distribution relative to the mean and
standard deviation. In this chapter we learned how
to use the standard normal probability distribution
to answer questions about all normal distributions.
Let’s return to distribution of IQ scores discussed in
the Section 6.1, “Intelligence Scores” (p. 313), and
try out some of our new knowledge.
•
k. What percentage of the SAT scores are below
450?
l.
What percentage of the SAT scores are above
575?
m. What SAT score is at the 95th percentile? Explain what this means.
Chapter Practice Test, which provides a formal self-evaluation of the mastery of the material before being tested in class. Correct responses are in the
back of the textbook.
y
independent events.
c. What percentage of the adult population has
“superior” intelligence?
d. What is the probability of randomly selecting
one person from this population who is classified below “average”?
e. What IQ score is at the 95th percentile? Explain what this means.
Chapter Practice Test
PART I: Knowing the Definitions
Answer “True” if the statement is always true. If
the statement is not always true, replace the words
shown in bold with words that make the statement
always true.
6.1 The normal probability distribution is symmetric about zero.
6.2
The total area under the curve of any normal
distribution is 1.0.
6.3
The theoretical probability that a particular
value of a continuous random variable will
occur is exactly zero.
The unit of measure for the standard score is
the same as the unit of measure of the
6.4
6.10 The most common distribution of a continuous random variable is the binomial probability.
PART II: Applying the Concepts
6.11 Find the following probabilities for z, the
standard normal score:
a. P (0 Ͻ z Ͻ 2.42)
b. P (z Ͻ 1.38)
c. P (z Ͻ Ϫ1.27)
d. P (Ϫ1.35 Ͻ z Ͻ 2.72)
6.12 Find the value of each z-score:
a. P(z Ͼ ?) ϭ 0.2643
b.
P(z Ͻ ?) ϭ 0.17
c. z(0.04)
6.13 Use the symbolic notation z(␣) to give the
symbolic name for each z-score shown in the
figure at the bottom of the page.
6.14 The lifetimes of flashlight batteries are normally distributed about a mean of 35.6 hr
with a standard deviation of 5.4 hr. Kevin selected one of these batteries at random and
tested it. What is the probability that this one
battery will last less than 40.0 hr?
6.15 The lengths of time, x, spent commuting
daily, one-way, to college by students are believed to have a mean of 22 min with a standard deviation of 9 min If the lengths of
xv
PREFACE
NEW and Updated MINITAB, Excel, and TI-83/84 instructions are introduced in the text alongside appropriate material. This approach allows instructors to choose which statistical technology, if any, they would like to incorporate
into their course.
NEW and Updated With more than 400 data sets, ranging from small to
large, students have the opportunity to practice using their statistical calculator
or computer.
Technology manuals offer additional instruction in these various statistical
technologies. Found on the Student’s Suite CD-ROM, as well as in StatisticsNow, our offerings include:
•
MINITAB Manual by Diane L. Benner and Linda M. Myers, Harrisburg Area
Community College.
•
Excel Manual by Diane L. Benner and Linda M. Myers, Harrisburg Area
Community College.
•
TI-83/84 Manual by Kevin Fox, Shasta College.
Note: These technology manuals are available in both print and electronic formats. Instructors, contact your sales representative to find out how these manuals can be custom published for your course.
166
CHAPTER 3 Descriptive Analysis and Presentation of Bivariate Data
SECTION 3.2 EXE RCISES
TE C H N O LO GY I N STR U CTI O N S: C O R R E LATI O N C O E FFI C I E NT
MINITAB (Release 14)
Input the x-variable data into C1 and the corresponding y-variable data into
C2; then continue with:
Choose:
Enter:
Stat Ͼ Basic Statistics Ͼ Correlation. . .
Variables: C1 C2 Ͼ OK
Input the x-variable data into column A and the corresponding y-variable
data into column B, activate a cell for the answer; then continue with:
Excel
Choose:
Enter:
Insert function, fx Ͼ Statistical Ͼ
Array 1: x data range
Array 2: y data range Ͼ OK
CORREL
Ͼ
OK
Datasets can be found on your Student’s Suite CD-ROM or at the
StatisticsNow website at .
3.3 [EX03-003] In a national survey of 500 business and 500 leisure travelers, each was asked
where they would most like “more space.”
Business
Leisure
On Airplane
Hotel Room
All Other
355
250
95
165
50
85
a. Express the table as percentages of the total.
TI-83/84 Plus
Input the x-variable data into L1 and the corresponding y-variable data into
L2; then continue with:
Choose:
Choose:
Enter:
2nd Ͼ CATALOG Ͼ DiagnosticOn* Ͼ
STAT Ͼ CALC Ͼ 8:LinReg(a ϩ bx)
L1, L2
ENTER
Ͼ
ENTER
*DiagnosticOn must be selected for r and r 2 to show. Once set, omit this step.
b. Express the table as percentages of the row totals. Why might one prefer the table to be expressed this way?
c. Express the table as percentages of the column
totals. Why might one prefer the table to be expressed this way?
3 4 Th “O tl
FIG U R E 3.9
Understanding the Linear Correlation Coefficient
The Data Window
The following method will create (1) a visual meaning for correlation, (2) a visual meaning for what the linear coefficient is measuring, and (3) an estimate
for r. The method is quick and generally yields a reasonable estimate when the
“window of data” is approximately square.
y
Note: This estimation technique does not replace the calculation of r. It is very
sensitive to the “spread” of the diagram. However, if the “window of data” is
approximately square, this approximation will be useful as a mental estimate
or check.
x
FIG U R E 3.10
Focusing on Pattern
Procedure
1. Construct a scatter diagram of your data, being sure to scale the axes so
that the resulting graph has an approximately square “window of data,”
as demonstrated in Figure 3.9 by the light green frame. The window may
not be the same region as determined by the bounds of the two scales
k f
b
i
t
l
”
hi
xvi
PREFACE
Working with Your Own
Data sections, appearing
at the end of each of the
four major parts of the
book, are designed to
encourage further
exploration, independent
student learning, and
critical thinking. These
can be used as individual
class projects or in small
groups.
392 CHAPTER 7 Sample Variability
Working with Your Own Data
Putting Probability to Work
5. Construct a histogram for this sampling distribution of sample means.
6. Calculate the mean xෆ and the standard error of the mean xෆ using the probability
distribution found in question 4.
7. Show that the results found in questions
1c, 5, and 6 support the three claims made
by the sampling distribution of sample
means and the central limit theorem. Cite
specific values to support your conclusions.
The sampling distribution of sample means and the
central limit theorem are very important to the development of the rest of this course. The proof,
which requires the use of calculus, is not included
in this textbook. However, the truth of the SDSM
and the CLT can be demonstrated both theoretically and by experimentation. The following activities will help to verify both statements.
A THE POPULATION
Consider the theoretical population that contains
the three numbers 0, 3, and 6 in equal proportions.
1. a. Construct the theoretical probability distribution for the drawing of a single number, with replacement, from this population.
b. Draw a histogram of this probability distribution.
C THE SAMPLING DISTRIBUTION,
EMPIRICALLY
Let’s now see whether the sampling distribution of
sample means and the central limit theorem can be
verified empirically; that is, does it hold when the
sampling distribution is formed by the sample
means that result from several random samples?
8. Draw a random sample of size 3 from the
given population. List your sample of three
numbers and calculate the mean for this
sample.
c. Calculate the mean, , and the standard
deviation, , for this population.
B THE SAMPLING DISTRIBUTION,
THEORETICALLY
Let’s study the theoretical sampling distribution
formed by the means of all possible samples of size
3 that can be drawn from the given population.
2. Construct a list showing all the possible samples of size 3 that could be drawn from this
population. (There are 27 possibilities.)
3. Find the mean for each of the 27 possible
samples listed in answer to question 2.
4. Construct the probability distribution (the
theoretical sampling distribution of sample
means) for these 27 sample means.
You may use a computer to generate your samples. You may take three identical “tags” numbered
0, 3, and 6, put them in a “hat,” and draw your
sample using replacement between each drawing.
Or you may use dice; let 0 be represented by 1 and
2; 3, by 3 and 4; and 6, by 5 and 6. You may also
use random numbers to simulate the drawing of
your samples. Or you may draw your sample from
the list of random samples at the end of this section. Describe the method you decide to use. (Ask
your instructor for guidance.)
9. Repeat question 8 forty-nine more times so
that you have a total of 50 sample means
that have resulted from samples of size 3.
Working WithYour Own Data
Here are 100 random samples of size 3 that
were generated by computer:
10. Construct a frequency distribution of the 50
sample means found in questions 8 and 9.
11. Construct a histogram of the frequency distribution of observed sample means.
12. Calculate the mean xෆ and standard deviation sxෆ of the frequency distribution formed
by the 50 sample means.
13. Compare the observed values of xෆ and sxෆ
with the values of xෆ and xෆ Do they agree?
Does the empirical distribution of xෆ look
like the theoretical one?
393
6
0
6
6
3
6
0
3
3
0
6
6
3
0
3
6
0
3
0
6
0
3
6
0
6
0
3
3
3
6
6
3
3
3
0
3
6
0
3
6
6
6
0
6
0
3
3
0
6
3
3
0
3
0
3
3
0
0
6
0
3
6
0
3
6
3
3
6
3
0
3
0
0
0
0
3
3
6
6
3
6
0
3
0
3
0
6
0
6
0
6
6
0
6
3
0
0
0
0
3
0
0
6
3
6
6
6
3
6
3
6
6
0
6
0
0
3
3
0
6
3
3
3
6
3
6
6
3
6
3
6
0
6
3
0
3
0
0
6
3
6
0
6
3
3
3
0
0
6
0
6
6
6
3
3
0
3
3
0
6
3
6
6
6
6
0
0
6
6
0
3
6
6
3
3
6
3
0
0
6
6
6
3
6
3
0
3
6
6
3
0
6
6
6
0
6
0
0
3
3
6
6
3
6
6
0
6
3
0
0
6
3
3
3
3
6
3
0
3
3
6
3
0
3
0
0
6
3
3
3
6
6
6
3
3
6
3
0
3
0
6
3
0
6
6
3
6
0
6
3
3
6
6
6
6
3
0
6
3
0
6
3
0
3
0
0
3
6
3
6
3
3
6
6
0
6
0
0
3
0
3
3
6
0
3
3
3
3
3
3
0
0
3
0
6
3
6
6
6
3
PREFACE
xvii
Learning Resources
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study time by building focused, chapter-by-chapter, Personalized Learning Plans
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•
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xviii
PREFACE
Learning Resources (continued)
Student’s Suite CD-ROM
(0-495-10533-3) This valuable learning resource includes:
•
Updated MINITAB Manual by Diane L. Benner and Linda
M. Myers, Harrisburg Community College.
•
Updated Excel Manual by Diane L. Benner and Linda M.
Myers, Harrisburg Area Community College.
•
Updated TI-83/84 Manual by Kevin Fox, Shasta College.
•
NEW and Updated Data sets formatted for MINITAB®,
Microsoft® Excel®, SPSS®, JMP®, SAS®, TI-83/84, and ASCII.
•
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can watch as an instructor walks them through key
examples from the text, step by step—giving a foundation
in the skills that they need to know. Each example found
on the CD-ROM is identified by icons located in the margin
of the text. Think of it as portable office hours!
vMentorTM allows students to talk (using
their own computer microphones) to tutors
who will skillfully guide them through a
problem using an interactive whiteboard
for illustration. Up to 40 hours of live
tutoring a week is available with every
new book and can be accessed through
.
PREFACE
xix
The Book Companion Website offers book- and course-specific resources, such
as tutorial quizzes for each chapter and data sets for exercises. Students can access the website through .
Updated Student Solutions Manual (0-495-10531-7), written by Patricia
Kuby, includes fully worked out solutions for all odd-numbered exercises and
also provides hints, tips, and additional interpretation for specific exercises.
Internet Companion for Statistics, written by Michael Larsen, from Iowa State
University, offers practical information on how to use the Internet to increase
students’ understanding of statistics. Organized by key topics covered in the introductory course, the text offers a brief review of a topic, listings of appropriate
websites, and study questions designed to build students’ analytical skills. This
can be accessed through .