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Index of Applications in Examples and Activities Act: Activity; Ex: Example Agriculture College Life Grape production: Ex 3.6 Strength of bark board: Ex 16.4 Tomato yield and planting density: Ex 15.12, Ex 15.13 Academic success of college sophomores: Ex 14.1 Advantages of multiple SAT scores in college admissions: Act 8.1 Asking questions in seminar class: Ex 6.5 Back-to-college spending: Ex 3.7 College attendance: Ex 10.12 College choice do-over: Ex 1.5 Comparing job offers: Ex 4.18 Detecting plagiarism: Ex 10.9 Enrollments at public universities: Ex 3.15 Gender of college students: Ex 8.7 Graduation rates: Ex 1.10, Ex 13.5, Ex 13.10 Graduation rates and student-related expenditures: Ex 5.1 Graduation rates at small colleges: Ex 14.6, Ex 14.7, Ex 14.8, Ex 14.9 How safe are college campuses? Ex 1.6 Impact of internet and television use on college student reading habits: Ex 9.2 Importance of college education: Ex 9.4 Internet use by college students: Ex 9.1 Math SAT score distribution: Ex 3.14 Misreporting grade point average: Ex 3.17 Money spent on textbooks: Ex 8.1 Predicting graduation rates: Ex 5.13 Roommate satisfaction: Ex 15.7 Students with jumper cables: Ex 7.22 Study habits of college seniors: Ex 3.5 Time required to complete registration: Ex 7.29 Travel distance to college: Ex 3.1 Tuition at public universities: Ex 3.9 Verbal SAT scores: Ex 3.21 Visits to class web site: Ex 4.3, Ex 4.4 Biology Age and flexibility: Act 5.2 Age of a lobster: Ex 5.19 Bee mating behavior: Ex 3.12, Ex 3.13 Black bear habitat selection: Ex 5.9 Calling behavior of Amazonian frogs: Ex 5.22 Cannibalism in wolf spiders: Ex 5.20, Ex 5.21 Charitable behavior of chimpanzees: Ex 9.10, Ex 11.7 Chirp rate for crickets: Ex 10.15 Distance deer mice will travel for food: Ex 5.7, Ex 5.10 Dominant and nondominant hands: Act 3.2 Egg weights: Ex 7.31 Head circumference at birth: Ex 4.19 Loon chick survival factors: Ex 5.17 Predator inspection in guppies: Ex 6.18 Recognizing your roommate’s scent: Ex 7.18 Reflexes with dominant and nondominant hands: Act 11.2 Repertoire size and body characteristics of nightingales: Ex 5.23 Scorpionfly courtship: Ex 8.4 Shark length and jaw width: Ex 13.11, Ex 13.12 Spider phobia: Ex 1.4 Business and Economics Application processing times: Ex 7.8 Cable services: Ex 6.22 Car sales: Ex 7.1 Christmas Price Index: Ex 3.22 Cost of Big Macs: Ex 4.7, Ex 4.8, Ex 4.12 Cost of energy bars: Ex 14.11 Cost of residential air-conditioning: Ex 15.8, Ex 15.9 Credit cards paid in full: Ex 7.21 Daily wasted time at work: Ex 10.14 Education level and income: Ex 3.23 Express mail volume: Ex 7.35 Hybrid car sales: Ex 12.3 Licensing example attempts: Ex 7.9 Mortgage choices: Ex 6.16 Predicting house prices: Ex 14.5 Price of fish: Ex 14.13 Prices of industrial properties: Ex 14.17, Ex 14.19 Resume typos: Ex 3.3 Starting salaries of business school graduates: Ex 16.11, Ex 16.12 Demography and Population Characteristics County population sizes: Ex 4.2 Head circumferences: Act 1.2 Heights and weights of American women: Ex 5.8 Heights of college athletes: Ex 1.1 Heights of mothers: Ex 4.17 Hitchhiker’s thumb: Ex 6.17 Median ages in 2030: Ex 3.10 Newborn birth weights: Ex 7.27 Percentage of population with higher education degrees: Ex 4.9, Ex 4.10 Two-child families: Ex 6.14 Women’s heights and number of siblings: Act 13.1 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Education and Child Development After-school activities: Ex 6.11 Chess lessons and memory improvement: Ex 11.6 Childcare for preschoolers: Ex 4.15 College plans of high school seniors: Ex 7.4 Combining exam scores: Ex 7.16 Helping hands: Ex 2.7, 2.9 IQ scores: Ex 4.16, Ex 7.28 Predictors of writing competence: Ex 14.4 School enrollment in Northern and Central Africa: Ex 3.11 Standardized test scores: Ex 4.14, Ex 10.16 Students’ knowledge of geography: Act 3.1 Television viewing habits of children: Ex 3.16 Environmental Science Cosmic radiation: Ex 9.7 Lead in tap water: Ex 10.7 Rainfall frequency distributions for Albuquerque: Ex 3.19 River water velocity and distance from shore: Ex 5.16 Soil and sediment characteristics: Ex 14.12, Ex 14.14, Ex 14.16 Water conservation: Ex 10.10 Water quality: Ex 1.2 Food Science Calorie consumption at fast food restaurants: Ex 2.2 Fat content of hot dogs: Ex 8.6 Fish food: Ex 5.15 Pomegranate juice and tumor growth: Ex 5.5 Tannin concentration in wine: Ex 5.2, Ex 5.6 Leisure and Popular Culture Car preferences: Ex 6.1 Do U Txt?: Ex 1.7 iPod shuffles: Ex 7.7 Life insurance for cartoon characters: Ex 2.3 Number of trials required to complete game: Ex 7.2 Probability a Hershey’s Kiss will land on its base: Act 6.1 Selecting cards: Ex 6.20 Selection of contest winners: Ex 6.7 Tossing a coin: Ex 6.8 Twitter words: Act 1.1 Manufacturing and Industry Bottled soda volumes: Ex 8.5 Comprehensive strength of concrete: Ex 7.14 Computer configurations: Ex 6.19 Computer sales: Ex 7.19 Corrosion of underground pipe coatings: Ex 15.14 Durable press rating of cotton fabric: Ex 14.18 DVD player warranties: Ex 6.24 Engineering stress test: Ex 7.3 Ergonomic characteristics of stool designs: Ex 15.10, Ex 15.11 Garbage truck processing times: Ex 7.30 GFI switches: Ex 6.12 Lifetime of compact florescent lightbulbs: Ex 10.2 On-time package delivery: Ex 10.18 Paint flaws: Ex 7.6 Testing for flaws: Ex 7.11, Ex 7.12 Marketing and Consumer Behavior Car choices: Ex 6.10 Energy efficient refrigerators: Ex 7.5 High-pressure sales tactics: Ex 16.13 Impact of food labels: Ex 10.8 Online security: Ex 7.20 Satisfaction with cell phone service: Ex 4.6 Medical Science Apgar scores: Ex 7.10, Ex 7.13 Affect of long work hours on sleep: Ex 11.10 Births and the lunar cycle: Ex 12.1, Ex 12.2 Blood platelet volume: Ex 8.2 Blood pressure and kidney disease: Ex 16.5 Blood test for ovarian cancer: Ex 10.6 Cardiovascular fitness of teens: Ex 10.11 Cerebral volume and ADHD: Ex 11.1 Chronic airflow obstruction: Ex 16.9 Contracting hepatitis from blood transfusion: Ex 8.8, Ex 8.9 Cooling treatment after oxygen deprivation in newborns: Ex 2.5 Diagnosing tuberculosis: Ex 6.15 Drive-through medicine: Ex 9.8 Effect of talking on blood pressure: Ex 11.4 Effects of ethanol on sleep time: Ex 15.6 Evaluating disease treatments: Ex 10.3 Facial expression and self-reported pain level: Ex 12.7 Growth hormone levels and diabetes: Ex 16.10 Hip-to-waist ratio and risk of heart attack: Ex 14.2 Hormones and body fat: Ex 15.4, Ex 15.5 Lead exposure and brain volume: Ex 5.12 Lyme disease: Ex 6.27 Markers for kidney disease: Ex 7.34 Maternal age and baby’s birth weight: Ex 13.2 Medical errors: Ex 6.9 Parental smoking and infant health: Ex 16.2, Ex 16.3 Passive knee extension: Ex 4.1 Platelet volume and heart attack risk: Ex 15.1, Ex 15.2, Ex 15.3 Premature births: Ex 7.36 Sleep duration and blood leptin level: Ex 13.13 Slowing the growth rate of tumors: Ex 10.5 Stroke mortality and education: Ex 12.8 Surviving a heart attack: Ex 6.13 Time perception and nicotine withdrawal: Ex 10.13 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Treating dyskinesia: Ex 16.8 Treatment for acute mountain sickness: Act 2.5 Ultrasound in treatment of soft-tissue injuries: Ex 11.5, Ex 11.8 Video games and pain management: Act 2.4 Vitamin B12 levels in human blood: Ex 16.7 Waiting time for cardiac procedures in Canada: Ex 9.9 Wart removal methods: Ex 11.9 Physical Sciences Rainfall data: Ex 7.33 Snow cover and temperature: Ex 13.8 Wind chill factor: Ex 14.3 Politics and Public Policy Fair hiring practices: Ex 6.29 Opinions on freedom of speech: Ex 11.11 Predicting election outcomes: Ex 13.3, Ex 13.6, Ex 13.7 Recall petition signatures: Act 9.3 Requests for building permits: Ex 6.31 School board politics: Ex 14.10 Support for affirmative action: Ex 9.1, Ex 9.4 Psychology, Sociology, and Social Issues Benefits of acting out: Ex 1.3 Color and perceived taste: Act 12.2 Estimating sizes: Act 1.3 Extrasensory perception: Ex 6.33 Gender and salary: Ex 11.2 Golden rectangles: Ex 4.11 Hand-holding couples: Ex 6.30 Internet addiction: Ex 6.28 Motivation for revenge: Ex 2.4 One-boy family planning: Ex 6.32 Reading emotions: Ex 11.3 Stroop effect: Act 2.2 Subliminal messages: Ex 2.5 Weight regained proportions for three follow-up methods: Ex 12.6 Public Health and Safety Careless or aggressive driving: Ex 9.5 Effect of cell phone distraction: Ex 2.8 Effects of McDonald’s hamburger sales: Act 2.3 Nicotine content of cigarettes: Ex 10.17 Safety of bicycle helmets: Ex 5.3 Salmonella in restaurant eggs: Act 7.2 Teenage driver citations and traffic school: Ex 6.23 Sports Age and marathon times: Ex 5.4, Ex 5.14 Calling a toss at a football game: Ex 6.6 Concussions in collegiate sports: Ex 12.4, Ex 12.5 Fairness of Euro coin-flipping in European sports: Act 6.2 Helium-filled footballs: Act 11.1 “Hot hand” in basketball: Act 6.3 Losing at golf: Ex 6.2, Ex 6.4 NBA player salaries: Ex 4.5, Ex 4.13 Olympic figure skating: Ex 3.20 Racing starts in competitive swimming: Ex 16.6 Soccer goalie action bias: Ex 6.26 Tennis ball diameters: Ex 10.1 Time to first goal in hockey: Ex 8.3 Treadmill time to exhaustion and ski time of biathletes: Ex 13.4, Ex 13.9 Wrestlers’ weight loss by headstand: Ex 13.1 Surveys and Opinion Polls Are cell phone users different?: Ex 2.1 Collecting and summarizing numerical data: Act 2.2 Designing a sampling plan: Facebook friending: Act 2.1 Selecting a random sample: Ex 2.2 Transportation Accidents by bus drivers: Ex 3.18 Airborne times for San Francisco to Washington D.C flight: Ex 9.3 Airline luggage weights: Ex 7.17 Airline passenger weights: Act 4.2 Automobile accidents by occupation: Ex 3.8 Comparing gasoline additives: Ex 2.10 Freeway traffic: Ex 7.15 Fuel efficiency of automobiles: Ex 16.1 Lost airline luggage: Ex 6.25 Motorcycle helmets: Ex 1.8, Ex 1.9 On-time airline flights: Ex 10.4 Predicting transit times: Ex 14.15 Turning directions on freeway off-ramp: Ex 6.3 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Statistics: The Exploration and Analysis of Data, Seventh Edition Roxy Peck, Jay L Devore Publisher: Richard Stratton Senior Sponsoring Editor: Molly Taylor Senior Developmental Editor: Jay Campbell Associate Editor: Daniel Seibert © 2012, 2008, 2005 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means, graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information 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World Inc Text designer: Rokusek Design Cover designer: RHDG Brooks/Cole 20 Channel Center Street Boston, MA 02210 USA Cover Image: © Joella Jean Mahoney/Red Stone Gallery Cengage Learning is a leading provider of customized learning solutions with oﬃce locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local oﬃce at: international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education, Ltd For your course and learning solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Printed in the United States of America 14 13 12 11 10 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Statistics The Exploration and Analysis of Data Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it To Beth Chance and Allan Rossman, whose dedication to improving statistics education is inspirational R P To Carol, Allie, and Teri J D About the Cover The cover image is by artist Joella Jean Mahoney, who paints striking abstract landscapes inspired by the American Southwest In her work, Mahoney is able to beautifully capture the underlying structure of rock formations and canyons In statistical analyses, we work to capture and learn from the underlying structure we find in data While the images we create are not nearly as beautiful as Mahoney’s work, in this sense we share a similar goal! Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Answers to Selected Odd-Numbered Exercises 11.33 a t ϭ 4.321, P-value Ϸ 0, reject H0 b t ϭ 1.662, P-value ϭ 0.055, fail to reject H0 c A smaller standard deviation in the sample of differences means that we have a lower estimate of the standard deviation of the population of differences Assuming that the mean wrist extensions for the two mouse types are the same (in other words, that the mean of the population of differences is zero), a sample mean difference of as much as 8.82 is much less likely when the standard deviation of the population of differences is around 10 than when the standard deviation of the population of differences is around 26 11.35 P-value ϭ 0.001, reject H0 11.37 z ϭ 21.667, P-value ϭ 0.048, reject H0 11.39 a z ϭ 1.172, P-value ϭ 0.121, fail to reject H0 b (20.036, 0.096) We are 99% confident that the difference between the proportion of Gen Y and the proportion of Gen X who made a donation via text message is between 20.036 and 0.096 In repeated sampling with random samples of size 400, approximately 99% of the resulting confidence intervals would contain the true difference in proportions who donated via text message 11.41 a z ϭ 20.298, P-value ϭ 0.766, fail to reject H0 b z ϭ 22.022, P-value ϭ 0.043, reject H0 c Assuming that the population proportions are equal, you are much less likely to get a difference in sample proportions as large as the one given when the samples are very large than when the samples are relatively small 11.43 a (20.078, 0.058) b Zero is included in the confidence interval This tells us that there is not convincing evidence of a difference between the proportions 11.45 No It is not appropriate to use the two-sample z test because the groups are not large enough We are not told the sizes of the groups, but we know that each is, at most, 81 The sample proportion for the fish oil group is 0.05, and 81(0.05) ϭ 4.05, which is less than 10 So, the conditions for the two-sample z test are not satisfied 11.47 z ϭ 0.767, P-value ϭ 0.443, fail to reject H0 11.49 (0.018, 0.082) Zero is not included in the confidence interval This means that we have convincing evidence at the 0.05 significance level of a difference between the proportions of people owning MP3 players in 2006 and 2005 11.51 z ϭ 6.306, P-value Ϸ 0, reject H0 11.53 z ϭ 3.800, P-value Ϸ 0, reject H0 11.55 a z ϭ 9.169, P-value Ϸ 0, reject H0 b No Since this is an observational study, causation cannot be inferred from the result 11.57 Since the data given are population characteristics, an inference procedure is not applicable It is known that the rate of Lou Gehrig’s disease among soldiers sent to the war is higher than for those not sent to the war 11.59 b If we want to know whether the e-mail intervention reduces (as opposed to changes) adolescents’ display of risk behavior in their profiles, then we use one-sided alternative hypotheses and the P-values are halved If that is the case, using a 0.05 significance level, we are convinced that the intervention is effective with regard to reduction of references to sex and that the proportion showing any of the three protective changes is greater for those receiving the e-mail intervention Each of the other two apparently reduced proportions could have occurred by chance 11.61 a t ϭ 26.565, P-value Ϸ 0, reject H0 b t ϭ 6.249, P-value Ϸ 0, reject H0 c t ϭ 0.079, P-value ϭ 0.937, fail to reject H0 This does not imply that students and faculty consider it acceptable to talk on a cell phone during class; in fact, the low sample mean ratings for both students and faculty show that both groups, on the whole, feel that the behavior is inappropriate 777 11.63 a t ϭ 217.382, P-value Ϸ 0, reject H0 b t ϭ 2.440, P-value ϭ 0.030, reject H0 c No, the paired t test would not be appropriate since the treatment and control groups were not paired samples 11.65 z ϭ 4.245, P-value Ϸ 0, reject H0 11.67 a t ϭ 211.952, P-value Ϸ 0, reject H0 b t ϭ 268.803, P-value Ϸ 0, reject H0 c t ϭ 0.698, P-value ϭ 0.494, fail to reject H0 11.69 t ϭ 0.856, P-value ϭ 0.210, fail to reject H0 11.71 t ϭ 21.336, P-value ϭ 0.193, fail to reject H0 11.73 z ϭ 21.263, P-value ϭ 0.103, fail to reject H0 11.75 (20.274, 20.082) We are 90% confident that p1 p2 lies between 20.274 and 20.082, where p1 is the proportion of children in the community with fluoridated water who have decayed teeth and p2 is the proportion of children in the community without fluoridated water who have decayed teeth The interval does not contain zero, which means that we have evidence at the 0.1 level of a difference between the proportions of children with decayed teeth in the two communities, and evidence at the 0.05 level that the proportion of children with decayed teeth is smaller in the community with fluoridated water 11.77 a (24.738, 22.738) b t ϭ 0.140, P-value ϭ 0.890, fail to reject H0 c t ϭ 20.446, P-value ϭ 0.330, fail to reject H0 11.79 a t ϭ 3.948, P-value Ϸ 0, reject H0 b t ϭ 21.165, P-value ϭ 0.249, fail to reject H0 11.81 z ϭ 5.590, P-value Ϸ 0, reject H0 Chapter 12 12.1 a P-value 0.024; H0 is not rejected b P-value 0.043; H0 is not rejected c P-value 0.035; H0 is not rejected d P-value 0.0002; H0 is rejected e P-value 0.172; H0 is not rejected 12.3 a P-value 0.0002 , 0.001, so H0 is rejected b The smallest expected count is 40(0.1) ϭ 4, which is less than The chisquare test would not be appropriate 12.5 X ϭ 19.599, P-value Ϸ 0, reject H0 12.7 X ϭ 457.464, P-value Ϸ 0, reject H0 12.9 a X ϭ 166.958, P-value Ϸ 0, reject H0 b X ϭ 5.052, P-value ϭ 0.025, reject H0 12.11 X ϭ 25.486, P-value Ϸ 0, reject H0 12.13 X ϭ 1.469, P-value ϭ 0.690, fail to reject H0 12.15 a P-value 0.844, fail to reject H0 b P-value 0.106, fail to reject H0 12.17 X ϭ 29.507, P-value ϭ 0.001, reject H0 12.19 a X ϭ 90.853, P-value Ϸ 0, reject H0 b The particularly high contributions to the chi-square statistic (in order of importance) come from the field of communication, languages, and cultural studies, in which there was a disproportionately high number of smokers; from the field of mathematics, engineering, and sciences, in which there was a disproportionately low number of smokers; and from the field of social science and human services, in which there was a disproportionately high number of smokers 12.21 a X ϭ 2.314, P-value ϭ 0.128, fail to reject H0 b Yes c Yes Since P-value 0.127 0.05, we not reject H0 d The two P-values are almost equal; in fact, the difference between them is only due to rounding errors in the Minitab program 12.23 a X ϭ 96.506, P-value Ϸ 0, reject H0 b The result of Part (a) tells us that the level of the gift seems to make a difference Looking at the data given, 12% of those receiving no gift made a Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 778 Answers to Selected Odd-Numbered Exercises donation, 14% of those receiving a small gift made a donation, and 21% of those receiving a large gift made a donation (These percentages can be compared to 16% making donations among the expected counts.) So, it seems that the most effective strategy is to include a large gift, with the small gift making very little difference compared to no gift at all 12.25 X ϭ 46.515, P-value Ϸ 0, reject H0 12.27 X ϭ 3.030, P-value ϭ 0.387, fail to reject H0 12.29 X ϭ 49.813, P-value Ϸ 0, reject H0 12.31 X ϭ 1.978, P-value ϭ 0.372, fail to reject H0 12.33 b X ϭ 8.034, P-value ϭ 0.005, reject H0 12.35 X ϭ 1.08, P-value ϭ 0.982, fail to reject H0 12.37 X ϭ 881.360, P-value Ϸ 0, reject H0 12.39 X ϭ 4.035, P-value ϭ 0.258, fail to reject H0 12.41 X ϭ 10.976, P-value Ͻ 0.001, reject H0 12.43 X ϭ 22.855, P-value Ϸ 0, reject H0 12.45 a X ϭ 8216.476, P-value Ϸ 0, reject H0 b This could occur if the birthrate is higher for the time of year designated as “Capricorn” than it is for other times of the year c The total number of policyholders listed in the first table is 460,168 Therefore, for example, the proportion of policyholders born under Aquarius is 35666 /460168 The total number of claims listed in the second table is 1000 So, if the numbers of claims were in proportion to the numbers of policyholders, then we would expect the number of claims for policyholders born under Aquarius to be 1000 135666 /4601682 77.506 This is the expected count for Aquarius, and the other expected counts are calculated in a similar way X ϭ 10.748, P-value ϭ 0.465, fail to reject H0 Chapter 13 13.1 a y 25.0 0.017x c 30.7 d 0.017 e 1.7 f No, the model should not be used to predict outside the range of the data 13.3 a When x 15, my 0.18 When x 17, my 0.186 b When x 15, P y 0.182 0.5 c When x 14, P y 0.1752 0.655, P 1y , 0.1782 0.579 13.5 a 47, 4700 b 0.3156, 0.0643 13.7 a 0.121 b se 0.155; This is a typical vertical deviation of a bone mineral density value in the sample from the value predicted by the least-squares line c 0.009 g/cm2 d 1.098 g /cm2 13.9 a r 0.883 b se 13.682, df ϭ 14 13.11 a The plot shows a linear pattern, and the vertical spread of points does not appear to be changing over the range of x values in the sample If we assume that the distribution of errors at any given x value is approximately normal, then the simple linear regression model seems appropriate b y^ 20.00227 1.247x; when x 0.09, y^ 0.110 c r 0.436, 43.6% of the variation in market share can be explained by the linear regression model relating market share and advertising share d se 0.0263, df ϭ 13.13 a 0.253 b 0.179; no c 13.15 a 0.1537 b (2.17, 2.83) c Yes, the interval is relatively narrow 13.17 a a ϭ 592.1, b ϭ 97.26 b When x 2, y^ 786.62, y y^ 229.62 c (87.76, 106.76) 13.19 t ϭ 23.66, P-value Ϸ 0, reject H0 13.21 a (0.081, 0.199) We are 95% confident that the mean change in pleasantness rating associated with an increase of impulse per second in firing frequency is between 0.081 and 0.199 b t ϭ 5.451, P-value ϭ 0.001, reject H0 13.23 a t ϭ 6.493, P-value Ϸ 0, reject H0 b t ϭ 1.56, P-value ϭ 0.079, fail to reject H0 13.25 t ϭ 217.57, P-value Ϸ 0, reject H0 13.27 a The plot supports the assumption that the simple linear regression model applies b Yes Since the normal probability plot shows a roughly linear pattern, it is reasonable to assume that the error distribution is approximately normal 13.29 a y^ 0.939 0.873x b The standardized residual plot shows that there is one point that is a clear outlier (the point whose standardized residual is 3.721) This is the point for product 25 c y^ 0.703 0.918x, removal of the point resulted in a reasonably substantial change in the equation of the estimated regression line d For every 1-cm increase in minimum width, the mean maximum width is estimated to increase by 0.918 cm The intercept would be an estimate of the mean maximum width when the minimum width is zero It is clearly impossible to have a container whose minimum width is zero e The pattern in this plot suggests that the variances of the y distributions decrease as x increases, and therefore that the assumption of constant variance is not valid 13.31 a There is one unusually large standardized residual, 2.52, for the point (164.2, 181) The point (387.8, 310) would seem to be an influential point b Apart from the one point that has a large residual, the arrangement of points in the residual plot seems consistent with the simple linear regression model c If we include the point with the unusually large standardized residual we might begin to suspect that the variances of the y distributions decrease as the x values increase However, from the relatively small number of points included we not have particularly strong evidence that the assumption of constant variance does not apply 13.33 A confidence interval is an estimate of the mean value of y when x ϭ x* A prediction interval is a prediction of an individual y value when x ϭ x* A prediction level of 95% means that the prediction interval has been calculated using a method that has a 5% error rate 13.35 a 4.038 b Since is the same distance from 2.5 as is 2, sa1b13.02 sa1b12.02 4.038 c 3.817 d x * x 2.5 13.37 a ( 6.532, 6.570) We are 95% confident that the mean milk pH when the milk temperature is 40°C is between 6.532 and 6.570 b (6.560, 6.616) c No, 90 is outside the range of x values in the data set 13.39 a y^ 20.001790 0.0021007x b (20.055, 20.032) c (20.097, 0.009) d The answer to Part (b) gives an interval in which we are 90% confident that the mean brain volume change for people with a childhood blood lead level of 20 mg/dL lies The answer to Part (c) states that if we were to find the brain volume change for one person with a childhood blood lead level of 20 mg/ dL, we are 90% confident that this value will lie within the interval found 13.41 a y^ 2133.02 5.92x b 1.127 c Yes Since the estimated slope is positive and since the P-value is small (given as 0.000 in the output) we have convincing evidence that the slope of the population regression line is positive d (173.252, 330.178) e It would not be appropriate to use the estimated regression line to predict the clutch size for a salamander with a snout-vent length of 105, since 105 is far outside the range of the x values in the original data set 13.43 a y^ 2.78551 0.04462x b t ϭ 10.848, P-value Ϸ 0, reject H0 c (3.672, 4.576); we are 95% confident that the moisture content for a box of cereal that has been on the shelf for 30 days will be between 3.672 and 4.576 percent d Since 4.1 is included in the confidence interval constructed in Part (c), a moisture content Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Answers to Selected Odd-Numbered Exercises exceeding 4.1 percent is quite plausible when the shelf time is 30 days 13.45 a (20.397, 20.193) b When x 0.5: (20.397, 2.0193); when x 0.7: (0.123, 0.323) c The simultaneous confidence level would be 100 2 112 % 98% d The simultaneous confidence level would be 100 152 % 85% 13.47 The statistic r is the correlation coefficient for a sample, while r denotes the correlation coefficient for the population 13.49 t ϭ 2.073, P-value ϭ 0.039, reject H0 13.51 a t ϭ 26.175, P-value Ϸ 0, reject H0 b Since r 120.262 0.0676, only 6.76% of the observed variation in grade point average would be explained by the regression line This is not a substantial percentage 13.53 t ϭ 1.855, P-value ϭ 0.106, fail to reject H0 13.55 a The slope of the estimated regression line for y ϭ verbal language score against x ϭ height gain from age 11 to 16 is 2.0 This tells us that for each extra inch of height gain the average verbal language score at age 11 increased by 2.0 percentage points The equivalent results for nonverbal language scores and math scores were 2.3 and 3.0 Thus the reported slopes are consistent with the statement that each extra inch of height gain was associated with an increase in test scores of between and percentage points b The slope of the estimated regression line for y ϭ verbal language score against x ϭ height gain from age 16 to 33 is 23.1 This tells us that for each extra inch of height gain the average verbal language score at age 11 decreased by 3.1 percentage points The equivalent results for nonverbal language scores and math scores were both 23.8 Thus the reported slopes are consistent with the statement that each extra inch of height gain was associated with a decrease in test scores of between 3.1 and 3.8 percentage points c Between the ages of 11 and 16 the first boy grew inches more than the second boy So the first boy’s age 11 math score is predicted to be # 15 percentage points higher than that of the second boy Between the ages of 16 and 33 the second boy grew inches more than the first boy According to this information the first boy’s age 11 math score is predicted to be # 3.8 19 percentage points higher than that of the second boy These two results are consistent with the conclusion that on the whole boys who did their growing early had higher cognitive scores at age 11 than those whose growth occurred later 13.57 a With t ϭ 23.399 and df ϭ 345, P-value ϭ 0.05 b Yes, we expect that those with greater coping humor ratings would have smaller depression ratings c No Since r 120.182 0.0324, we know that only 3.2% of the variation in depression scale values is attributable to the approximate linear relationship with the coping humor scale So the linear regression model will generally not give accurate predictions 13.59 a t ϭ 26.090, P-value Ϸ 0, reject H0 b A 95% prediction interval is (21.667, 7.856) Other prediction levels are possible c No For x 10 the least-squares line predicts y 22.58 Since it is not possible to have a negative trail length, it is clear that the simple linear regression model does not apply at x 10 So the simple linear regression model is not suitable for this prediction 13.61 a t ϭ 0.488, P-value ϭ 0.633, fail to reject H0 b A 95% confidence interval is (47.076, 54.106) Other confidence levels are possible 13.63 H0: b br, Ha: b br, t ϭ 21.03457, P-value ϭ 0.320, fail to reject H0; we not have convincing evidence that the slopes of the population regression lines for the two different frog populations are not equal 13.65 If the point (20, 33000) is not included, then the slope of the least-squares line would be relatively small and negative (appear- 779 ing close to horizontal when drawn to the scales of the scatterplot given in the question) If the point is included then the slope of the least-squares line would still be negative, but much further from zero 13.67 The small P-value indicates that there is convincing evidence of a useful linear relationship between percentage raise and productivity 13.69 a The values e1, p , en are the vertical deviations of the y observations from the population regression line The residuals are the vertical deviations from the sample regression line b False The simple linear regression model states that the mean value of y is equal to a bx c No You only test hypotheses about population characteristics; b is a sample statistic d Strictly speaking this statement is false, since a set of points lying exactly on a straight line will give a zero result for SSResid However, it is certainly true to say that, since SSResid is a sum of squares, its value must be nonnegative e This is not possible, since the sum of the residuals is always zero f This is not possible, since SSResid (here said to be equal to 731) is always less than or equal to SSTo (here said to be 615) Cumulative Review 13 CR13.1 Randomly assign the 400 students to two groups of equal size, Group A and Group B Have the 400 students take the same course, attending the same lectures and being given the same homework assignments The only difference between the two groups should be that the students in Group A should be given daily quizzes and the students in Group B should not After the final exam the exam scores for the students in Group A should be compared to the exam scores for the students in Group B CR13.3 b The two airlines with the highest numbers of fines assessed may not be the worst in terms of maintenance violations since these airlines might have more flights than the other airlines CR13.5 a (0.651, 0.709) We are 95% confident that the proportion of all adult Americans who view a landline phone as a necessity is between 0.651 and 0.709 b z ϭ 1.267, P-value ϭ 0.103, fail to reject H0 c z ϭ 9.513, P-value Ϸ 0, reject H0 CR13.7 a 0.62 b 0.1216 c 0.19 d 0.0684 CR13.9 b y^ 212.887 21.126x d t ϭ 21.263, P-value Ϸ 0, reject H0 CR13.11 X ϭ 26.175, P-value Ϸ 0, reject H0 CR13.13 X ϭ 15.106, P-value ϭ 0.002, reject H0 CR13.15 t ϭ Ϫ113.17, df ϭ 45, P-value Ϸ 0, reject H0 CR13.17 X ϭ 4.8, P-value ϭ 0.684, fail to reject H0 Chapter 14 14.1 A deterministic model does not have the random deviation component e, while a probabilistic model does contain such a component 14.3 a (mean y value for fixed values of x1, x2, x3) ϭ 30 0.90x1 0.08x2 4.5x3 b b0 30, b1 0.9, b2 0.08, b3 24.50 c The average change in acceptable load associated with a 1-cm increase in left lateral bending, when grip endurance and trunk extension ratio are held fixed, is 0.90 kg d The average change in acceptable load associated with a N/kg increase in trunk extension ratio, when grip endurance and left lateral bending are held fixed, is 24.5 kg e 23.5 f 95% Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 780 Answers to Selected Odd-Numbered Exercises 14.5 a 13.552 g b When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.828 g When width is fixed, the mean increase in weight associated with a 1-mm increase in length is 0.373 g 14.7 a 103.11 b 96.87 c b1 26.6; 6.6 is the expected decrease in yield associated with a one-unit increase in mean temperature when the mean percentage of sunshine remains fixed b2 24.5; 4.5 is the expected decrease in yield associated with a one-unit increase in mean percentage of sunshine when mean temperature remains fixed 14.9 b Higher for x ϭ 10 c When the degree of delignification increases from to the mean chlorine content increases by Mean chlorine content decreases by when degree of delignification increases from to 10 14.11 c The parallel lines in each graph are attributable to the lack of interaction between the two independent variables 14.13 a y a b1x1 b2x2 b3x3 e b y a b1x1 b2x2 b3x3 b4x 21 b5x 22 b6x 23 e c y a b1x1 b2x2 b3x3 b4x1x2 e; y a b1x1 b2x2 b3x3 b4x1x3 e; y a b1x1 b2x2 b3x3 b4x2x3 e d y a b1x1 b2x2 b3x3 b4x 21 b5x 22 b6x 23 b7x1x2 b8x1x3 b9x2x3 e 14.15 a Three dummy variables would be needed to incorporate a nonnumerical variable with four categories For example, you could define x3 ϭ if the car is a subcompact and otherwise, x4 ϭ if the car is a compact and otherwise, and x5 ϭ if the car is a midsize and otherwise The model equation is then y a b1x1 b2x2 b3x3 b4x4 b5x5 e b For the variables defined in Part (a), x6 ϭ x1x3, x7 ϭ x1x4, and x8 ϭ x1x5 are the additional predictors needed to incorporate interaction between age and size class 14.17 a 0.01 Ͻ P-value Ͻ 0.05 b P-value Ͼ 0.10 c P-value ϭ 0.01 d 0.001 Ͻ P-value Ͻ 0.01 14.19 a F ϭ 12118, P-value ≈ 0, reject H0 b Since the P-value is small and r is close to 1, there is strong evidence that the model is useful c The model in Part (b) should be recommended, since adding the variables x1 and x2 to the model [to obtain the model in Part (a)] only increases the value of R2 a small amount (from 0.994 to 0.996) 14.21 F ϭ 24.41, P-value Ͻ 0.001, reject H0 and conclude that the model is useful 14.23 F ϭ 3.5, 0.01 Ͻ P-value Ͻ 0.05, reject H0 and conclude that the model is useful 14.25 F ϭ 7.986, P-value Ͻ 0.001, reject H0 and conclude that the model is useful 14.27 a y^ 1.44 0.0523length 0.00397speed b 1.3245 c F ϭ 24.02, P-value ≈ 0, reject H0 and conclude that the model is length useful d y^ 1.59 1.40a b e The model in part (a) has speed R 0.75 and R adjusted 0.719, whereas the model in part (d) has R2 0.543 and R adjusted 0.516 14.29 a SSResid ϭ 390.4347, SSTo ϭ 1618.2093, SSRegr ϭ 1227.7746 b R ϭ 0.759; this means that 75.9% of the variation in the observed shear strength values has been explained by the fitted model c F ϭ 5.039, 0.01 Ͻ P-value Ͻ 0.05, reject H0, and conclude that the model is useful 14.31 F ϭ 96.64, P-value Ͻ 0.001, reject H0, and conclude that the model is useful 14.35 y^ 35.8 0.68x1 1.28x2, F ϭ 18.95, P-value Ͻ 0.001, reject H0, and conclude that the model is useful Chapter 15 15.1 a 0.001 Ͻ P-value Ͻ 0.01 b P-value Ͼ 0.10 c P-value ϭ 0.01 d P-value Ͻ 0.001 e 0.05 Ͻ P-value Ͻ 0.10 f 0.01 Ͻ P-value Ͻ 0.05 (using df1 ϭ and df2 ϭ 60) 15.3 a H0:m1 m2 m3 m4, Ha: At least two of the four mi’s are different b P-value ϭ 0.012, fail to reject H0 c P-value ϭ 0.012, fail to reject H0 15.5 F ϭ 6.687, P-value ϭ 0.001, reject H0 15.7 F ϭ 5.273, P-value ϭ 0.002, reject H0 15.9 F ϭ 53.8, P-value Ͻ 0.001, reject H0 15.11 F ϭ 2.62, 0.05 Ͻ P-value Ͻ 0.10, fail to reject H0 15.13 Source of Variation Treatments Error Total df 16 19 Sum of Squares 75,081.72 235,419.04 310,500.76 Mean Square F 25,027.24 14,713.69 1.70 F ϭ 1.70, P-value Ͼ 0.10, fail to reject H0 15.15 Since there is a significant difference in all three of the pairs we need a set of intervals none of which includes zero Set is therefore the required set 15.17 a In decreasing order of the resulting mean numbers of pretzels eaten the treatments were: slides with related text, slides with no text, slides with unrelated text, and no slides There were no significant differences between the results for slides with no text and slides with unrelated text, and for slides with unrelated text and no slides However there was a significant difference between the results for slides with related text and each one of the other treatments, and between the results for no slides and for slides with no text (and for slides with related text) b The results for the women and men are almost exactly the reverse of one another, with, for example, slides with related text (treatment 2) resulting in the smallest mean number of pretzels eaten for the women and the largest mean number of pretzels eaten for the men For the men, treatment was significantly different from all the other treatments; however for women treatment was not significantly different from treatment For both women and men there was a significant difference between treatments and and no significant difference between treatments and However, between treatments and there was a significant difference for the women but no significant difference for the men 15.19 a Sample mean Driving 42 Shooting 4.00 Fighting 5.30 Sample mean Driving 2.81 Shooting 3.44 Fighting 4.01 b 15.21 a F ϭ 45.64, P-value Ϸ 0, reject H0 b Yes; T-K interval is (0.388, 0.912) Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Index 781 Index in k systematic sample, 45 A Additive multiple regression model, general, 672–673 Additive probabilistic model, 612–613 Adjusted coefficient of multiple determination (R2), 689 Alternative hypothesis, 458–460 Ambiguity and survey questions, 72 ANOVA see Single-factor analysis of variance (ANOVA) Axis, broken, 148 B Bar chart for categorical data, 15 comparative see Comparative bar chart other uses for, 96–98 Bell-shaped curve, 122 Bias in sampling, 38–39 Bivariate data see also Categorical data cautions and limitations, 286–287 defined, 11 example, 12 examples of interpreting results of, 284–286 reporting results of analysis of, 284 Bivariate data set defined, 133 scatterplot of, 212–213, 214 unusual points in, 241 Bivariate normal distribution, 654–656 Blocking defined, 53 diagram of, 61 example, 54 extraneous variables and, 54 overview, 50 random assignment and, 62 Bound on error of estimation defined, 426–427 sample size choice and, 440–441 Boxplot activity, 205 comparative, 189 modified, 186–188 skeletal, 184–185 small sample sizes and, 203 C Categorical data activity, 152 bar chart for, 14–15 chi-square tests for, 574–582 comparative bar charts and, 90–91 defined, 11 differences in counts and, 577 frequency distribution for, 13–14 notation for, 574–575 numerical summary quantities for, 171 pie charts and, 91–94 summarizing results of, 586 Categorical data set, 573 Categorical variable defined, 334 examples, 334–336 with more than two categories, 681 in multiple regression models, 679–681 testing for independence of more than two, 596 testing for independence of two, 592–596 Causation association and, 526–527 correlation and, 220 Cause-and-effect, determining, 33–34 Cell count see also Expected cell count; Observed cell count displaying, 588 in a two-way frequency table, 587 Census, 38 Center of data set describing, 164 interpreting, 190–196 Central Limit Theorem confidence intervals and, 432 sampling distribution and, 395–396 Chebyshev’s Rule, 191–193 Chi-square distribution, 578 Chi-square statistic formula for, 582 homogeneity test and, 587 Chi-square test cautions and limitations, 603–604 for homogeneity testing, 587 statistical analysis reporting and, 601–602 for univariate data, 574–582 CI see Confidence interval (CI) Class interval defined, 116 density, 119 example, 116–117 Cluster, 44 Cluster sampling, 44–45 Coefficient of determination, 241–245 Coefficient of multiple determination (R2), 688 Common population proportion, 551 Comparative bar chart activity, 152 example, 91 vs pie chart, 94 for visual comparisons, 90 Comparative boxplot, 188 Comparative notation for population or treatment means, 516 for population or treatment proportions, 549 Complete second-order model, 677 Completely randomized design, 61 Comprehension, survey respondents and, 71 Conclusion, drawing from statistical studies, 34–35 Conditional probability, 317–318 Confidence interval (CI) for a bx, 648 activity, 450–451, 452–453 781 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 782 Index Confidence interval (CI) (continued ) of b, 626–628 cautions and limitations, 448–449 for comparing population or treatment means using independent samples, 527–529 for comparing population or treatment means using paired samples, 542–544 for comparing population or treatment proportions, 555–556 defined, 419 example, 421–422, 648–649 general form of, 425–426 for large populations, 421 large-sample, for a population proportion, 424 for a mean y value, 648–649 for normal distributions, 420 normal distributions and, 432 one-sample, 431–432 prediction interval and, 650–651 probability and, 422–423 published data and standard deviation, 446–447 published data and two-sample, 561 statistical analysis reporting and, 445 unknown population standard deviation and, 433, 435–440 Confidence level activity, 449–451 defined, 419 for a population proportion, 424–425 Confounded variables, 50 Confounding variable, 33 Contingency table, 586 Continuous data defined, 13 frequency distribution for, 116–117 histograms for, 117–121 Continuous numerical variable defined, 336 population models for, 342–348 summarizing, 337–338 Continuous probability distribution defined, 343–344 examples, 344–348 Control, of variables, 50 Control group, 57, 66 Convenience sampling, 46 Correlation activity, 290 causation and, 220 types of coefficients, 212–220 Correlation and regression technology activity, 290 Correlation coefficient checking normality with, 369–370 defined, 212 examples, 214–218, 244–245 reporting the value of, 284 Cumulative relative frequency, 125–127 Cumulative relative frequency plot, 126–128 Curve, finding using transformations, 264–265 D Danger of extrapolation least-squares lines and, 227, 228 simple linear regression and, 621–622 Data see also specific types defined, 11 sensible collection, 31 types, 10–13 Data analysis process, Data collection issues activity, 565–566 for experimental studies, 77 limitations, 77–78 for observational studies, 76–77 Data set describing the center, 164 describing variability in, 175–181 summarizing, 184–188 Degree of freedom, 179 ANOVA and, 708–709 chi-square distributions and, 578 sample comparison and, 518 simple linear regression and, 620 t distributions and, 434–435 test power and Type II error probabilities, 500–501 two-sample t test and, 526 Density, class interval, 119 Density curve, 344 Density histogram, 337–338, 343 Density scale, 119 Dependent outcome, 305–306 Dependent variable, 223 Descriptive statistics, Deterministic relationship, 612 Diagram of experimental designs, 58–62 Dichotomous variable, 679–680 Dichotomy, 171 Direct control defined, 53 example, 54, 56 extraneous variables and, 54 overview, 50 Discrete data, 13, 106–121 Discrete numerical variable, 340 Distribution see specific types Dotplot, 16–18 Double-blind experiment, 60 Dummy variable, 679–680 E Empirical estimation, 316–319 Empirical Rule abnormal distribution and, 203 defined, 193 example, 194 z score and, 195 Error sum of squares, 708 Estimated regression line, 646–651 Estimation activity, 26–27, 81 choosing a statistic for computing, 413–416 large-sample, for a population proportion, 418–428 point, 412–416 standard deviation and bias and, 416 Event see also specific types Expected cell count computing, 590 defined, 575 Experiment activity, 80 data collection issues, 77 defined, 33, 49 double-blind, 68 example, 56, 57 pre-questions, 62 single-blind, 67–68 using a control group, 57, 66 using volunteers, 68 well-defined requirements, 50 Experimental condition, 49 Experimental design activity, 81 evaluating, 56–57 goal of, 65 underlying structure of, 58–62 Experimental unit defined, 58 replication and, 68 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Index Experimentation and data collection, 32–33 Explanatory variable defined, 49, 53 in regression analysis, 223 Extraneous variable dealing with, 54 defined, 50 Extreme outlier, 185 Extreme values identifying, 356–358 in normal distributions, 363–364 F F distribution ANOVA and, 709–710 defined, 690–691 F test for model utility, 691–696 Factor in comparisons, 704 defined, 32, 33 Fitted value see Predicted value Five-number summary, 185 Fixed number properties, 614 Frequency, 13 Frequency distribution area and, 146–147 for categorical data, 13–14 compacting, 113 for continuous numerical data, 116–117 example, 14, 112 grouping data, 114–115 uses, 111 Full quadratic model, 677 Fundamental identity for single-factor ANOVA, 713 G General additive multiple regression model, 672–673 Golden ratio for rectangles, 187 Goodness-of-fit statistic, 577 Goodness-of-fit test chi-square distributions and, 578–582 for homogeneity, 589 for independence of more than two categorical variables, 596 for independence of two categorical variables, 592–594 Grand total in a two-way frequency table, 586 Graphical display cautions and limitations, 146–149 interpreting, 143–145 for statistical reporting, 142–143 H Heavy-tailed curve, 122 Histogram for continuous numerical data and equal class interval widths, 118–119 for continuous numerical data and unequal class interval widths, 119, 120 for discrete numerical data, 113 example, 4, 5, 113–114 grouping data, 115 sample, 123 shapes, 121–123 tails, 122 using density, 121 Homogeneity, 587–592 Hypothesis see also specific types defined, 458 testing about treatment differences, 523 Hypothesis test for b, 628–629 cautions and limitations, 504–505, 563 defined, 458 errors in, 463–464 interpreting published data for, 503–504 interpreting results of, 503 large-sample, for a population proportion, 468–479 for a population mean, 482–490 population proportions and, summary, 476 power of see Hypothesis test power purpose, 461 sample comparison and, 518–523 significance level of, 464 steps for, 477 summarizing results of, 503 Hypothesis test power calculating, 496–497 defined, 493–494 effects of factors on, 494–495 for testing hypotheses about proportions, 498 Type II error probabilities and, 495–496 783 I Inappropriate actions in data interpretation, 77–78 Independence (variable), 592–596 Independent outcome defined, 305–306 multiplication rule for, 306–307 Independent sample, 517, 536 Independent variable, 223 Indicator variable, 679–680 Inferential statistics defined, objective of, 411 Influential observation, 239, 241 Information retrieval and survey respondents, 73 Interaction predictor, 677 Intercept, 223 Interquartile range, 179–180 Interval estimate see Confidence interval (CI) J Jittering, 275 L Large-sample confidence interval for a population proportion, 418–426 for proportion differences, 555–556 Large-sample confidence interval for p, 424 alternative to, 425 alternative to, activity, 452 Large-sample test for comparison problems, 550–555 computing a P-value for, 473–476 Leaf, numerical data and, 101 Least-squares estimate, 686–687 Least-squares line see also Sample regression line defined, 225 deviations from, 235 example, 226–228, 228–229 population regression line and, 617 predicting value of y with, 230 slope of, 226, 625–632 standard deviation about, 245–248 weighted, 639 Least-squares principle regression function fit and, 686 straight lines and, 224–226 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 784 Index Line assessing fit of, 234–248 equation of, 223 fitting straight, 224–226 goodness of fit, 225 graphs of, 224 least-squares principle and, 224–226 Linear regression bivariate data and, 223–230 simple model for, 612–622 Linear relationship strength, 216 Logistic regression binary variables and, 274–286 data transformation and, 278–281 equation for, 276–277 Lurking variable, 54 M Margin of error, 446 Marginal total in a two-way frequency table, 586 Mean see also specific types combining with standard deviation, 190–191 comparison of, 516 defined, 164 denoting, 165 deviations from, 175–177 example, 165 vs median, 168–169 outliers and, 167 Mean square, 708–709 Mean value of a difference in means, 517 of a numerical variable, 338–340 Measurement bias, 38, 39 Measures of relative standing, 194–195 Median defined, 167 example, 168 vs mean, 168–169 outliers and, 168 as percentile, 195 Memory and survey respondents, 73 Mild outlier, 185 Minitab jittering and, 275 numerical descriptive measures from, 168 outliers and, 187 Model utility test for independence in a bivariate normal population, 656 for simple linear regression, 629–632 Modified boxplot, 186–187 Multimodal histogram, 112 Multiple comparisons procedure, 717–721 Multiple regression model activity, 701 defined, 671 example, 673, 678–679 fitting, 685–687 general additive, 672–673 model utility F test for, 691 polynomial, 674–676 utility of, 688–696 variable interaction in, 677 Multivariate data defined, 11 goodness-of-fit testing and, 596 N Nonlinear relationships and transformations, 253–274 Nonresponse bias, 38–40 Normal curve, 122, 350 Normal distribution activities, 380–381 defined, 350–351 extreme values in, 363–364 nonstandard, 358–362 standard see Standard normal distribution vs t distribution (activity), 506–507 Normal probability distribution, 347–348 Normal probability plot population normality and, 367–369 standardized residuals and, 636–638, 642–644 Normality, 367–375 Null hypothesis categorical data analysis and, 575 defined, 458–461 example, 459, 460–461 population mean comparison and, 518–519, 522 Numerical data activity, 204 defined, 11 displaying bivariate, 133–139 dotplots for, 16–18 example, 13 frequency distribution for continuous, 116–121 histograms for, 116–121 stem-and-leaf displays and, 101–107 types, 12 Numerical summary measures see also specific types cautions and limitations, 202–203 interpreting, 201 for statistical reporting, 199–201 Numerical variable, 334, 336 O Observational study data collection and, 32–33 data collection issues, 76–77 defined, 33, 526 difficulties with, 527 surveys and, 70–74 Observed cell count, 586, 588 Observed significance level see P-value One-sample t confidence interval for comparison problems, 542–544 for a population mean, 435–440 One-sample t test, 485–489 One-sample z confidence interval, 431 One-way frequency table, 576 Outlier boxplots and, 185 defined, 103 example report after removal, 145 numerical summary measures and, 203 observation as, 241 Overcoverage, 76 P Paired data benefits of using, 544 defined, 18 Paired sample defined, 517, 536 example, 537–548 methods of inference for, 538 Paired t confidence interval, 543 Paired t statistic, 542 Paired t test, 538–542 Parabola, quadratic functions and, 254 Pearson’s sample correlation coefficient see also Correlation coefficient defined, 213 example, 219 properties of, 216 Percentile, 195–196 Pie chart activity, 152 categorical summaries and, 91 categorical variables and, 93–94 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Index vs comparative bar chart, 94 constructing, 92–93 example, 92 other uses for, 96–97 vs segmented bar graph, 95 Placebo, 66–67 Placebo effect, 67 Placebo treatment, 84 Point estimation defined, 412 example, 412–413 sample selection and, 418 simple linear regression and, 617, 619 statistical analysis reporting and, 445 Point prediction interpreting, 619 simple linear regression and, 617 Polynomial regression curve descriptions for, 256 as multiple regression model, 674–676 nonlinear relationships and, 253–255 Pooled t test, 526 Population comparing using a categorial variable, 590 defined, 7, 334 test of homogeneity when comparing, 589–594 Population correlation coefficient defined, 219–220 inferences about, 654–656 Population data and sampling, 123–125 Population distribution, 334 Population interquartile range, 181 Population mean comparing using independent samples, 511–531 comparing using paired samples, 536–544 confidence interval for, 431–441 defined, 165 example, 166 hypothesis tests for, 482–490 one-sample t test for, 485–489 Population proportion large-sample difference inferences for, 549–556 large-sample hypothesis tests for, 468–479 of S’s, denoting, 171 Population regression coefficient, 673 Population regression function for general additive multiple regressions, 673 for polynomial regressions, 675 Population regression line defined, 613 estimating, 617–620 Population regression line slope estimating, 625 least-squares line slope and, 625–632 Population standard deviation, 178 Population variance, 178 Power transformation, 265–269 Power transformation ladder, 266 Practical significance, 489–490 Predicted value example, 236–237 obtaining, 235 reporting, 284 Prediction interval for a single y value, 650–651 Predictor variable, 223 Principle of least squares fitting a straight line and, 224–226 regression function fit and, 686 Probabilistic model, 612–613 Probability activities, 328 basic properties of, 303–305 calculating for any normal distribution, 359–362 calculating others for z, 354–355 conditional, 317–318 decision-making and, 312–315 defined, 301, 302 dependent outcomes and, 305–306 estimating empirically, 316–319 estimating using simulation, 319–324 hypothesis testing and, 471–472 improving approximation of, 343 independent outcomes and, 305–307 normal plot and plausibility of, 367 notation for, 336 of an outcome, 302 relative frequency interpretation of, 302–304 subjective interpretation of, 302 Probability distribution see Continuous probability distribution Probability of success, 276 Probability rules, 308–309 Proportion, example comparison of, 591–592 785 Published data bivariate data and, 284 chi-square tests and, 602–603 confidence intervals and, 561–563 interpreting graphical displays, 145–146 interpreting hypotheses tests, 503–504 interpreting numerical summary measures, 201 interval estimates and, 446–447 two-sample hypothesis tests and, 561–563 P-value calculating, 474–479 computing and alternative hypotheses, 473 defined, 471 determining with a z test statistic, 475 finding for a t test, 483–484 goodness-of-fit statistic and, 578 indications of size of, 472–473 significance levels and, 473 two-sample t test and, 526 two-tailed tests and, 474 Q Quadratic model, 255–256 Quadratic regression computing, 254–255 example, 256–258 Quadratic regression model, 675 Qualitative data, 11 Qualitative variable predictor, 679–681 testing for independence of more than two, 596 testing for independence of two, 592–596 Quantitative data, 11 Quartile defined, 179 example, 180 as percentiles, 195 R r see Pearson’s sample correlation coefficient Random assignment activity, 82 defined, 53 diagram of, 60 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 786 Index Random assignment (continued) example, 54, 56 extraneous variables and, 54 overview, 51–52 performing, 54–56 Random mechanism, 55 Random number, simulations and, 320–324 Random sample, simple defined, 40 selecting, 41–42 Random sampling example, 42 goal, 43 overview, 40–43 stratified, 44 Randomized controlled experiment, 527 Range of a data set, 175 Rectangle, golden ratio for, 187 Reexpression see Transformation Regression, 229–230 Regression analysis see also Linear regression; Multiple regression model activity, 660 defined, 230 example, 628 objective of, 223, 671 test for independence and, 656 variable interaction in, 676–679 Regression coefficient, 675 Regression sum of squares, 691 Relative frequency area and, 146–147 combining multiple, 117 cumulative, 125–128 equation, 13 example of use, 91 Relative frequency distribution comparative bar charts and, 90–91 defined, 13 histograms and, 336–337 Replication defined, 52, 53 example, 54, 56, 57 purpose, 68 Research study evaluation, 8–9 Residual defined for a multiple regression model, 688 defined for a regression line, 235 example, 236–237 plotting, 237–241, 638–644 Residual analysis example, 637–638 simple linear regression and, 636–638 Residual plot defined, 237, 638 example, 238, 239–240, 640 standardized, 638–644 Residual sum of squares defined for a multiple regression model, 688 defined for a regression line, 242 example, 242–243 Response bias, 38, 39 Response reporting and survey respondents, 73–74 Response variable defined, 49, 53 in regression analysis, 223 Right-tailed curve, 122 S Sample defined, independent, 517, 536 paired, 517, 536 Sample mean defined, 164 deviations from, 175–177 example, 165 sampling distribution of, 390–399 Sample median, 168 Sample proportion of successes comparison properties of, 550 confidence intervals and, 419 defined, 171 for large populations, 401–404 purpose, 401 Sample regression line, 225, 229 see also Least-squares line Sample size bound on error of estimation and, 426–427, 440–441 as a reflection of the whole, 43–44 Sample standard deviation, 177–178 Sample variance, 177–178 Sampling see also specific types activity, 79–80 bias in, 38–39 random, 40–43 with replacement, 42 selection process, 37–38 variability, 123–125 without replacement, 42 Sampling distribution of a ϩ bx, 647 defined, 389 of a sample mean, 390–399 of a sample proportion, 401–405, 419–420 of x1 x2, 517–518 Sampling distribution of x activity, 407–409 confidence intervals for population means and, 431 general properties of, 394–396 for nonnormal small populations, 396–397, 399 for normal large populations, 391–392 purpose, 385 for skewed populations, 392–393 for small populations, 397–398 Sampling frame, 41 Sampling variability, 386–388 Scatterplot axes intersection, 136–137 bivariate data and, 212–213, 214 defined, 133 example, 134–135 interpreting patterns in, 149 simple linear regression and, 617 Segmented bar graph, 95–96 Selection bias, 38–39 Sequence of trials defined, 52 diagram of, 59 example, 66 Significance level defined, 464 P-values and, 473 Simple linear regression activity, 660 example, 616 model utility test for, 629–632 Simple linear regression model basic assumptions of, 614 cautions and limitations, 659 checking adequacy of, 635–644 confidence interval for b and, 626 confidence intervals and, 648 defined, 613 equation for, 636 estimated standard deviation of statistic b and, 626 example, 630–632 key assumption of, 622 key features of, 614–615 population regression line and, 625–632 property insights for, 616–617 published data and, 658–659 residual analysis and, 636–638 scatterplot patterns with, 617 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Index Simple random sample defined, 40 selecting, 41–42 Simulation activities, 328 approximating probabilities with, 321 defined, 319 examples, 321–324 Simultaneous confidence level, 720 Single-blind experiment, 67–68 Single-factor analysis of variance (ANOVA) activity, 725–727 assumptions for, 707 defined, 704–705 example, 706, 722–723 F test for, 710–712 notation in, 705 summarizing, 712–714 Skeletal boxplot, 184–185 Skewed histogram, 122 Slope defined, 223 of least-squares line, 226 point estimates of for population regression line, 617 Smoothed histogram, 121 Squared deviation line fit and, 225 variance and, 177–178 Stacked bar graph see Segmented bar graph Standard deviation about the least-squares line, 245–248 combining with mean, 190–191 defined, 177, 178 estimated, 620–622 estimated, of the statistic a bx, 647 estimated, of the statistic b, 626 example, 177–178 of a numerical variable, 338–340 as statistical standard error, 426 Standard error, 426, 446 Standard normal curve, 351 Standard normal curve area finding, 353–354 probability and, 355–357 using the table of, 352 Standard normal distribution defined, 351 working with, 352 Standardization, 195 Standardized residual defined, 636 example, 637–638 plot examples, 640–644 Standardized score see Z score Standardizing endpoints, 358 Statistic biased, 414–416 defined, 386 standard error of, 426 unbiased, 414–416 Statistic a + bx, 647 Statistic b estimated standard deviation of, 626 linear regression model slope coefficient and, 625 properties of sampling distribution of, 625 Statistical analysis chi-square test interpretation and, 601–602 confidence intervals for reporting, 445 graphical displays for reporting, 142–143 interpreting graphical displays, 143–145 interpreting numerical summaries, 200 interpreting population characteristic estimates, 445–446 interpreting results of, 283–287 interpreting two-sample confidence intervals, 561 numerical measures for reporting, 199–200 point estimates for reporting, 445 published data and graphical displays, 145–146 published data and numerical measures, 201 published data and simple linear regression models, 658–659 Statistical significance, 489–490 Statistical study drawing conclusions from, 34–35 experimentation, 32–33 observation, 32–33 purpose, 76 Statistics defined, process of using, 2, purpose, 1, Stem, numerical data and, 101 787 Stem-and-leaf display activity, 152–153 alternative display types, 104 comparative, 106 constructing, 103 defined, 101 example, 102–103 optimal number of items, 104 repeating stems, 105 uses, 103 Strata, 44 Stratified random sampling, 44 Stroop effect, 80 Studentized range distribution, 718 Survey, 71 Survey respondent’s tasks, 71–74 Symmetric histogram, 121–122 Systematic sampling, 44 T t distribution degrees of freedom and, 434–435 vs normal distribution (activity), 506–507 properties of, 434 sample comparison and, 518 t test for bivariate normal populations, 655 finding P-values for, 483–484 one-sample for a population mean, 485–489 paired, 538–542 pooled for population comparison, 526 power of and Type II error probabilities, 499–501 two-sample for population comparison, 519–522 two-sample for treatment comparison, 523–526 Table of standard normal curve areas, 352–353 Test procedure, hypothesis defined, 458 power of see Hypothesis test power process of, 471 purpose, 462, 468–471 for sample comparison, 518–523 Test statistic defined, 471 P-value determination and z, 475–476 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 788 Index Time-series plot defined, 138 examples, 138–139 unequal spacing in, 148–149 Total sum of squares ANOVA and, 713 defined for a multiple regression model, 689 defined for a regression line, 242 example, 242–243 Transformation see also specific types common types, 261 defined, 258–259, 370–371 example, 259–260, 261–264 example of power, 267–269 example of reversing, 265 finding curves using, 264–265 logarithmic, 372–374 logistic regression and, 278–281 normalizing, 367–375 power, 265–266 selecting, 374–375 square-root, 371 Treatment comparing, 523–526 comparing using a categorical variable, 588 defined, 49, 53 test of homogeneity when comparing, 588–592 Treatment mean comparing using independent samples, 511–531 comparing using paired samples, 536–544 Treatment proportion, 549–556 Treatment sum of squares, 708 Trimmed mean, 169–170 Trimming percentage, 169 Tukey-Kramer (T-K) multiple comparisons procedure defined, 717–718 example, 718–719, 721–722 results summary of, 721 simultaneous confidence level and, 720 Two-sample t confidence interval defined, 527–528 example, 528–529 Two-sample t statistic, 542 Two-sample t test improper use of, 541 for population comparison, 519–522 for treatment comparison, 523–526 Two-sample test activity, 565 cautions and limitations, 563 Two-sample z test, 553–555 Two-way frequency table activity, 606 defined, 586 Two-way table, 585–586 Type I error defined, 463 examples, 463–464 probability of, 464–466 Type II error defined, 463 examples, 464–466 probability of, 464 probability of, and t test power, 499–501 probability of, and test power, 493–501 U Undercoverage defined, 38 results of, 76 Uniform distribution, 345 Unimodal histogram, 121 Univariate data chi-square tests for categorical, 574–582 defined, 11 stem-and-leaf displays for, 101 V Variability activity, 26, 204 data set range and, 175 deviations from the mean, 175–177 interpreting, 190–196 nature and role, 3–5 sample variance and, 177 Variable see also specific types binary and logistic regression, 274 confounded, 50 confounding, 33 defined, 11 direct control of, 50 explanatory, 49, 53 extraneous, 50, 54 interaction between multiple, 676–679 lurking, 54 qualitative predictor, 679–681 in regression analysis, 223 relationship description of two, 612–613 response, 49, 53 test for independence of, 654–656 Variance defined, 177 of a difference of independent quantities, 517 Vertical intercept, 223 Voluntary response sampling, 46 Volunteer subjects, 68 Y y-intercept defined, 223 point estimates of for population regression line, 617 Z Z curve, 351 Z score converting to an x value, 364–365 defined, 194 Empirical Rule and, 195 interpreting, 362 Pearson’s sample correlation coefficient and, 213 standardizing endpoints with, 358 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Tabulated area = probability Standard normal probabilities (cumulative z curve areas) z* Standard normal (z) curve z* 00 01 02 03 04 05 06 07 08 09 23.8 23.7 23.6 23.5 0001 0001 0002 0002 0001 0001 0002 0002 0001 0001 0001 0002 0001 0001 0001 0002 0001 0001 0001 0002 0001 0001 0001 0002 0001 0001 0001 0002 0001 0001 0001 0002 0001 0001 0001 0002 0000 0001 0001 0002 23.4 23.3 23.2 23.1 23.0 0003 0005 0007 0010 0013 0003 0005 0007 0009 0013 0003 0005 0006 0009 0013 0003 0004 0006 0009 0012 0003 0004 0006 0008 0012 0003 0004 0006 0008 0011 0003 0004 0006 0008 0011 0003 0004 0005 0008 0011 0003 0004 0005 0007 0010 0002 0003 0005 0007 0010 22.9 22.8 22.7 22.6 22.5 0019 0026 0035 0047 0062 0018 0025 0034 0045 0060 0018 0024 0033 0044 0059 0017 0023 0032 0043 0057 0016 0023 0031 0041 0055 0016 0022 0030 0040 0054 0015 0021 0029 0039 0052 0015 0021 0028 0038 0051 0014 0020 0027 0037 0049 0014 0019 0026 0036 0048 22.4 22.3 22.2 22.1 22.0 0082 0107 0139 0179 0228 0080 0104 0136 0174 0222 0078 0102 0132 0170 0217 0075 0099 0129 0166 0212 0073 0096 0125 0162 0207 0071 0094 0122 0158 0202 0069 0091 0119 0154 0197 0068 0089 0116 0150 0192 0066 0087 0113 0146 0188 0064 0084 0110 0143 0183 21.9 21.8 21.7 21.6 21.5 0287 0359 0446 0548 0668 0281 0351 0436 0537 0655 0274 0344 0427 0526 0643 0268 0336 0418 0516 0630 0262 0329 0409 0505 0618 0256 0322 0401 0495 0606 0250 0314 0392 0485 0594 0244 0307 0384 0475 0582 0239 0301 0375 0465 0571 0233 0294 0367 0455 0559 21.4 21.3 21.2 21.1 21.0 0808 0968 1151 1357 1587 0793 0951 1131 1335 1562 0778 0934 1112 1314 1539 0764 0918 1093 1292 1515 0749 0901 1075 1271 1492 0735 0885 1056 1251 1469 0721 0869 1038 1230 1446 0708 0853 1020 1210 1423 0694 0838 1003 1190 1401 0681 0823 0985 1170 1379 20.9 20.8 20.7 20.6 20.5 1841 2119 2420 2743 3085 1814 2090 2389 2709 3050 1788 2061 2358 2676 3015 1762 2033 2327 2643 2981 1736 2005 2296 2611 2946 1711 1977 2266 2578 2912 1685 1949 2236 2546 2877 1660 1922 2206 2514 2843 1635 1894 2177 2483 2810 1611 1867 2148 2451 2776 20.4 20.3 20.2 20.1 20.0 3446 3821 4207 4602 5000 3409 3783 4168 4562 4960 3372 3745 4129 4522 4920 3336 3707 4090 4483 4880 3300 3669 4052 4443 4840 3264 3632 4013 4404 4801 3228 3594 3974 4364 4761 3192 3557 3936 4325 4721 3156 3520 3897 4286 4681 3121 3483 3859 4247 4641 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Tabulated area = probability Standard normal probabilities (continued) Standard normal (z) curve z* z* 00 01 02 03 04 05 06 07 08 09 0.0 0.1 0.2 0.3 0.4 5000 5398 5793 6179 6554 5040 5438 5832 6217 6591 5080 5478 5871 6255 6628 5120 5517 5910 6293 6664 5160 5557 5948 6331 6700 5199 5596 5987 6368 6736 5239 5636 6026 6406 6772 5279 5675 6064 6443 6808 5319 5714 6103 6480 6844 5359 5753 6141 6517 6879 0.5 0.6 0.7 0.8 0.9 6915 7257 7580 7881 8159 6950 7291 7611 7910 8186 6985 7324 7642 7939 8212 7019 7357 7673 7967 8238 7054 7389 7704 7995 8264 7088 7422 7734 8023 8289 7123 7454 7764 8051 8315 7157 7486 7794 8078 8340 7190 7517 7823 8106 8365 7224 7549 7852 8133 8389 1.0 1.1 1.2 1.3 1.4 8413 8643 8849 9032 9192 8438 8665 8869 9049 9207 8461 8686 8888 9066 9222 8485 8708 8907 9082 9236 8508 8729 8925 9099 9251 8531 8749 8944 9115 9265 8554 8770 8962 9131 9279 8577 8790 8980 9147 9292 8599 8810 8997 9162 9306 8621 8830 9015 9177 9319 1.5 1.6 1.7 1.8 1.9 9332 9452 9554 9641 9713 9345 9463 9564 9649 9719 9357 9474 9573 9656 9726 9370 9484 9582 9664 9732 9382 9495 9591 9671 9738 9394 9505 9599 9678 9744 9406 9515 9608 9686 9750 9418 9525 9616 9693 9756 9429 9535 9625 9699 9761 9441 9545 9633 9706 9767 2.0 2.1 2.2 2.3 2.4 9772 9821 9861 9893 9918 9778 9826 9864 9896 9920 9783 9830 9868 9898 9922 9788 9834 9871 9901 9925 9793 9838 9875 9904 9927 9798 9842 9878 9906 9929 9803 9846 9881 9909 9931 9808 9850 9884 9911 9932 9812 9854 9887 9913 9934 9817 9857 9890 9916 9936 2.5 2.6 2.7 2.8 2.9 9938 9953 9965 9974 9981 9940 9955 9966 9975 9982 9941 9956 9967 9976 9982 9943 9957 9968 9977 9983 9945 9959 9969 9977 9984 9946 9960 9970 9978 9984 9948 9961 9971 9979 9985 9949 9962 9972 9979 9985 9951 9963 9973 9980 9986 9952 9964 9974 9981 9986 3.0 3.1 3.2 3.3 3.4 9987 9990 9993 9995 9997 9987 9991 9993 9995 9997 9987 9991 9994 9995 9997 9988 9991 9994 9996 9997 9988 9992 9994 9996 9997 9989 9992 9994 9996 9997 9989 9992 9994 9996 9997 9989 9992 9995 9996 9997 9990 9993 9995 9996 9997 9990 9993 9995 9997 9998 3.5 3.6 3.7 3.8 9998 9998 9999 9999 9998 9998 9999 9999 9998 9999 9999 9999 9998 9999 9999 9999 9998 9999 9999 9999 9998 9999 9999 9999 9998 9999 9999 9999 9998 9999 9999 9999 9998 9999 9999 9999 9998 9999 9999 1.0000 Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it t critical values t curve Central area – t critical value 80% 80% 3.08 1.89 1.64 1.53 1.48 90% 90% 6.31 2.92 2.35 2.13 2.02 95% 95% 12.71 4.30 3.18 2.78 2.57 98% 98% 31.82 6.97 4.54 3.75 3.37 99% 99% 63.66 9.93 5.84 4.60 4.03 998% 99.8% 318.31 23.33 10.21 7.17 5.89 999% 99.9% 636.62 31.60 12.92 8.61 6.86 10 1.44 1.42 1.40 1.38 1.37 1.94 1.90 1.86 1.83 1.81 2.45 2.37 2.31 2.26 2.23 3.14 3.00 2.90 2.82 2.76 3.71 3.50 3.36 3.25 3.17 5.21 4.79 4.50 4.30 4.14 5.96 5.41 5.04 4.78 4.59 11 12 13 14 15 1.36 1.36 1.35 1.35 1.34 1.80 1.78 1.77 1.76 1.75 2.20 2.18 2.16 2.15 2.13 2.72 2.68 2.65 2.62 2.60 3.11 3.06 3.01 2.98 2.95 4.03 3.93 3.85 3.79 3.73 4.44 4.32 4.22 4.14 4.07 16 17 18 19 20 1.34 1.33 1.33 1.33 1.33 1.75 1.74 1.73 1.73 1.73 2.12 2.11 2.10 2.09 2.09 2.58 2.57 2.55 2.54 2.53 2.92 2.90 2.88 2.86 2.85 3.69 3.65 3.61 3.58 3.55 4.02 3.97 3.92 3.88 3.85 21 22 23 24 25 1.32 1.32 1.32 1.32 1.32 1.72 1.72 1.71 1.71 1.71 2.08 2.07 2.07 2.06 2.06 2.52 2.51 2.50 2.49 2.49 2.83 2.82 2.81 2.80 2.79 3.53 3.51 3.49 3.47 3.45 3.82 3.79 3.77 3.75 3.73 26 27 28 29 30 1.32 1.31 1.31 1.31 1.31 1.71 1.70 1.70 1.70 1.70 2.06 2.05 2.05 2.05 2.04 2.48 2.47 2.47 2.46 2.46 2.78 2.77 2.76 2.76 2.75 3.44 3.42 3.41 3.40 3.39 3.71 3.69 3.67 3.66 3.65 40 60 120 1.30 1.30 1.29 1.68 1.67 1.66 2.02 2.00 1.98 2.42 2.39 2.36 2.70 2.66 2.62 3.31 3.23 3.16 3.55 3.46 3.37 ؕ 1.28 1.645 1.96 2.33 2.58 3.09 3.29 Central area captured: Conﬁdence level: Degrees of freedom z critical values t critical value Copyright 2010 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it ... the ordering of topics in the ﬁrst ten chapters of the book mirrors this process: data collection, then data description, then statistical inference The logical order in the data analysis process... Variability in the Data Unlike many introductory texts, Statistics: The Exploration and Analysis of Data, Seventh Edition, is organized in a manner consistent with the natural order of the data analysis. .. cengagebrain.com At the CengageBrain.com home page, search for the ISBN of your title (from the back cover of your book) using the search box at the top of the page This will take you to the product
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Xem thêm: The exploration analysis of data , The exploration analysis of data , 3: Statistics and the Data Analysis Process, 4: Types of Data and Some Simple Graphical Displays, ACTIVITY 1.2: Head Sizes: Understanding Variability, 1: Statistical Studies: Observation and Experimentation, 4: More on Experimental Design, 5: More on Observational Studies: Designing Surveys (Optional), 6: Interpreting and Communicating the Results of Statistical Analyses, ACTIVITY 2.5: Be Careful with Random Assignment!, 1: Displaying Categorical Data: Comparative Bar Charts and Pie Charts, 2: Displaying Numerical Data: Stem-and-Leaf Displays, 3: Displaying Numerical Data: Frequency Distributions and Histograms, 4: Displaying Bivariate Numerical Data, 5: Interpreting and Communicating the Results of Statistical Analyses, 1: Describing the Center of a Data Set, 2: Describing Variability in a Data Set, 3: Summarizing a Data Set: Boxplots, 4: Interpreting Center and Variability: Chebyshev’s Rule, the Empirical Rule, and z Scores, ACTIVITY 4.1: Collecting and Summarizing Numerical Data, 2: Linear Regression: Fitting a Line to Bivariate Data, 3: Assessing the Fit of a Line, 4: Nonlinear Relationships and Transformations, ACTIVITY 5.1: Exploring Correlation and Regression Technology Activity (Applets), 1: Interpreting Probabilities and Basic Probability Rules, 2: Probability as a Basis for Making Decisions, 3: Estimating Probabilities Empirically and by Using Simulation, ACTIVITY 6.3: The “Hot Hand” in Basketball, 1: Describing the Distribution of Values in a Population, 2: Population Models for Continuous Numerical Variables, 4: Checking for Normality and Normalizing Transformations, 1: Statistics and Sampling Variability, 2: The Sampling Distribution of a Sample Mean, 3: The Sampling Distribution of a Sample Proportion, ACTIVITY 8.1: Do Students Who Take the SATs Multiple Times Have an Advantage in College Admissions?, 2: Large-Sample Confidence Interval for a Population Proportion, 3: Confidence Interval for a Population Mean, 4: Interpreting and Communicating the Results of Statistical Analyses, ACTIVITY 9.3: Verifying Signatures on a Recall Petition, 1: Hypotheses and Test Procedures, 2: Errors in Hypothesis Testing, 3: Large-Sample Hypothesis Tests for a Population Proportion, 4: Hypothesis Tests for a Population Mean, 5: Power and Probability of Type II Error, ACTIVITY 10.1: Comparing the t and z Distributions, 1: Inferences Concerning the Difference Between Two Population or Treatment Means Using Independent Samples, 2: Inferences Concerning the Difference Between Two Population or Treatment Means Using Paired Samples, 3: Large-Sample Inferences Concerning the Difference Between Two Population or Treatment Proportions, ACTIVITY 11.2: Thinking About Data Collection, 1: Chi-Square Tests for Univariate Data, 2: Tests for Homogeneity and Independence in a Two-way Table, 3: Interpreting and Communicating the Results of Statistical Analyses, ACTIVITY 12.2: Color and Perceived Taste, 1: Simple Linear Regression Model, 2: Inferences About the Slope of the Population Regression Line, 4: Inferences Based on the Estimated Regression Line (Optional), 5: Inferences About the Population Correlation Coefficient (Optional), ACTIVITY 13.1: Are Tall Women from “Big” Families?, 2: Fitting a Model and Assessing Its Utility, ACTIVITY 14.1: Exploring the Relationship Between Number of Predictors and Sample Size, 1: Single-Factor ANOVA and the F Test