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©2008 maxfield foundation this selection and arrangement of content is licensed under the creative commons attribution license http creativecommons.org/licenses/by/2.0/[close]
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table of contents preface 1 author ackowledgements 5 student welcome letter 6 1 sampling and data 1.1 sampling and data 7 1.2 statistics .7 1.3 probability 9 1.4 key terms 9 1.5 data 11 1.6 sampling 12 1.7 variation 17 1.8 answers and rounding off 18 1.9 frequency 18 1.10 summary 23 1.11 practice sampling and data .25 1.12 homework 28 1.13 lab 1 data collection 36 1.14 lab 2 sampling experiment 38 solutions 41 2 descriptive statistics 2.1 descriptive statistics 43 2.2 displaying data 43 2.3 stem and leaf graphs stemplots 44 2.4 histograms 45 2.5 box plots 48 2.6 measures of the location of the data 51 2.7 measures of the center of the data 54 2.8 skewness and the mean median and mode 56 2.9 measures of the spread of the data 57 2.10 summary of formulas .64 2.11 practice 1 center of the data 65 2.12 practice 2 spread of the data .68 2.13 homework 69 2.14 lab descriptive statistics 84 solutions 86 3 probability topics 3.1 probability topics 93 3.2 terminology 94 3.3 independent and mutually exclusive events 95 3.4 two basic rules of probability 97 3.5 contingency tables 100 3.6 venn diagrams optional 103 3.7 tree diagrams optional 105 3.8 summary of formulas .109 3.9 practice 1 contingency tables 110 3.10 practice 2 calculating probabilities 112[close]
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iv 3.11 homework 113 3.12 review 121 3.13 lab probability topics 124 solutions 127 4 discrete random variables 4.1 discrete random variables 133 4.2 probability distribution function pdf for a discrete random variable 134 4.3 mean or expected value and standard deviation 135 4.4 common discrete probability distribution functions 138 4.5 binomial 138 4.6 geometric optional 141 4.7 hypergeometric optional 143 4.8 poisson 146 4.9 summary of functions 148 4.10 practice 1 discrete distribution 150 4.11 practice 2 binomial distribution 151 4.12 practice 3 poisson distribution 153 4.13 practice 4 geometric distribution 154 4.14 practice 5 hypergeometric distribution 156 4.15 homework 157 4.16 review 165 4.17 lab 1 discrete distribution playing card experiment 168 4.18 lab 2 discrete distribution lucky dice experiment 172 solutions 176 5 continuous random variables 5.1 continuous random variables 183 5.2 continuous probability functions 184 5.3 the uniform distribution 186 5.4 the exponential distribution 190 5.5 summary of the uniform and exponential probability distributions 196 5.6 practice 1 uniform distribution 197 5.7 practice 2 exponential distribution 200 5.8 homework 202 5.9 review 207 5.10 lab continuous distribution 210 solutions 213 6 the normal distribution 6.1 the normal distribution 217 6.2 the standard normal distribution 218 6.3 z-scores 218 6.4 areas to the left and right of x 220 6.5 calculations of probabilities 220 6.6 summary of formulas .224 6.7 practice the normal distribution 225 6.8 homework 227 6.9 review 232 6.10 lab 1 normal distribution lap times 234 6.11 lap 2 normal distribution pinkie length 236 solutions 240 7 the central limit theorem[close]
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v 7.1 the central limit theorem 243 7.2 the central limit theorem for sample means averages 244 7.3 the central limit theorem for sums 246 7.4 using the central limit theorem 248 7.5 summary of formulas .253 7.6 practice the central limit theorem 254 7.7 homework 257 7.8 review 263 7.9 lab 1 central limit theorem pocket change 265 7.10 lab 2 central limit theorem cookie recipes 269 solutions 274 8 confidence intervals 8.1 confidence intervals 277 8.2 confidence interval single population mean population standard deviation known normal 279 8.3 confidence interval single population mean standard deviation unknown student-t 282 8.4 confidence interval for a population proportion 284 8.5 summary of formulas .288 8.6 practice 1 confidence intervals for averages known population standard deviation 289 8.7 practice 2 confidence intervals for averages unknown population standard deviation 291 8.8 practice 3 confidence intervals for proportions 293 8.9 homework 295 8.10 review 304 8.11 lab 1 confidence interval home costs 308 8.12 lab 2 confidence interval place of birth 310 8.13 lab 3 confidence interval womens heights 312 solutions 314 9 hypothesis testing single mean and single proportion 9.1 hypothesis testing single mean and single proportion 321 9.2 null and alternate hypotheses 322 9.3 outcomes and the type i and type ii errors 323 9.4 distribution needed for hypothesis testing 324 9.5 assumption 325 9.6 rare events 325 9.7 using the sample to support one of the hypotheses 325 9.8 decision and conclusion 327 9.9 additional information 327 9.10 summary of the hypothesis test 328 9.11 examples 329 9.12 summary of formulas 340 9.13 practice 1 single mean known population standard deviation 341 9.14 practice 2 single mean unknown population standard deviation 343 9.15 practice 3 single proportion 345 9.16 homework 347 9.17 review 359 9.18 lab hypothesis testing of a single mean and single proportion 362 solutions 366 10 hypothesis testing two means paired data two proportions 10.1 hypothesis testing two population means and two population proportions 373[close]
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vi 10.2 comparing two independent population means with unknown population standard deviations 374 10.3 comparing two independent population means with known population standard deviations 377 10.4 comparing two independent population proportions 379 10.5 matched or paired samples 381 10.6 summary of types of hypothesis tests 386 10.7 practice 1 hypothesis testing for two proportions 387 10.8 practice 2 hypothesis testing for two averages 389 10.9 homework 391 10.10 review 401 10.11 lab hypothesis testing for two means and two proportions 404 solutions 409 11 the chi-square distribution 11.1 the chi-square distribution 415 11.2 notation 416 11.3 facts about the chi-square distribution 416 11.4 goodness-of-fit test 417 11.5 test of independence 424 11.6 test of a single variance optional 427 11.7 summary of formulas 430 11.8 practice 1 goodness-of-fit test 431 11.9 practice 2 contingency tables 433 11.10 practice 3 test of a single variance 435 11.11 homework 437 11.12 review 443 11.13 lab 1 chi-square goodness-of-fit 448 11.14 lab 2 chi-square test for independence 453 solutions 455 12 linear regression and correlation 12.1 linear regression and correlation 461 12.2 linear equations 461 12.3 slope and y-intercept of a linear equation 463 12.4 scatter plots 463 12.5 the regression equation 466 12.6 the correlation coefficient 469 12.7 facts about the correlation coefficient for linear regression 470 12.8 prediction 472 12.9 outliers 473 12.10 95 critical values of the sample correlation coefficient table 478 12.11 summary 480 12.12 practice linear regression 481 12.13 homework 484 12.14 lab 1 regression distance from school 497 12.15 lab 2 regression textbook cost 500 12.16 lab 3 regression fuel efficiency 503 solutions 507 13 f distribution and anova 13.1 f distribution and anova 511 13.2 anova 511[close]
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vii 13.3 the f distribution and the f ratio 512 13.4 facts about the f distribution 513 13.5 test of two variances 517 13.6 summary 519 13.7 practice anova 520 13.8 homework 522 13.9 review 523 13.10 lab anova 527 solutions 529 14 appendix 14.1 practice final exam 1 531 14.2 practice final exam 2 540 14.3 data sets 549 14.4 group projects 552 14.5 solution sheets 563 14.6 english phrases written mathematically 567 14.7 symbols and their meanings 568 14.8 formulas 573 solutions 575 ti-83 and ti-84 calculator instructions 579 glossary .589 index 597[close]
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preface 1 welcome to collaborative statistics presented by connexions the initial section below introduces you to connexions if you are familiar with connexions please skip to about collaborative statistics section about connexions about connexions connexions modular content connexions cnx.org2 is an online open access educational resource dedicated to providing high quality learning materials free online free in printable pdf format and at low cost in bound volumes through print-on-demand publishing the collaborative statistics textbook is one of many collections available to connexions users each collection is composed of a number of re-usable learning modules written in the connexions xml markup language each module may also be re-used or re-purposed as part of other collections and may be used outside of connexions including collaborative statistics connexions currently offers over 6000 modules and more than 350 collections the modules of collaborative statistics are derived from the original paper version of the textbook under the same title collaborative statistics each module represents a self-contained concept from the original work together the modules comprise the original textbook re-use and customization the creative commons cc attribution license3 applies to all connexions modules under this license any module in connexions may be used or modified for any purpose as long as proper attribution to the original authors is maintained connexions authoring tools make re-use or re-purposing easy therefore instructors anywhere are permitted to create customized versions of the collaborative statistics textbook by editing modules deleting unneeded modules and adding their own supplementary modules connexions authoring tools keep track of these changes and maintain the cc license s required attribution to the original authors this process creates a new collection that can be viewed online downloaded as a single pdf file or ordered in any quantity by instructors and students as a low-cost printed textbook to start building custom collections please visit the help page create a collection with existing modules 4 for a guide to authoring modules please look at the help page create a module in minutes 5 read the book online print the pdf or buy a copy of the book to browse the collaborative statistics textbook online visit the collection home page at cnx.org/content/col10522/latest6 you will then have three options 1 this content is available online at[close]
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2 1 you may obtain a pdf of the entire textbook to print or view offline by clicking on the download pdf link in the content actions box 2 you may order a bound copy of the collection by clicking on the order printed copy button 3 you may view the collection modules online by clicking on the start link which takes you to the first module in the collection you can then navigate through the subsequent modules by using their next and previous links to move forward and backward in the collection you can jump to any module in the collection by clicking on that module s title in the collection contents box on the left side of the window if these contents are hidden make them visible by clicking on show table of contents accessibility and section 508 compliance · for information on general connexions accessibility features please visit http cnx.org/content/m17212/latest/7 · for information on accessibility features specific to the collaborative statistics textbook please visit http cnx.org/content/m17211/latest/8 version change history and errata · for a list of modifications http cnx.org/content/m17360/latest/9 updates and corrections please visit about collaborative statistics collaborative statistics was written by barbara illowsky and susan dean faculty members at de anza college in cupertino california the textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes courses using this textbook have been articulated by the university of california for transfer of credit the textbook contains full materials for course offerings including expository text examples labs homework and projects a teacher s guide is currently available in print form and on the connexions site at http cnx.org/content/col10547/latest10 the on-line text for both collections will meet the section 508 standards for accessibility an on-line course based on the textbook was also developed by illowsky and dean it has won an award as the best on-line california community college course the on-line course will be available at a later date as a collection in connexions and each lesson in the on-line course will be linked to the on-line textbook chapter the on-line course will include in addition to expository text and examples videos of course lectures in captioned and non-captioned format the original preface to the book as written by professors illowsky and dean now follows this book is intended for introductory statistics courses being taken by students at two and fouryear colleges who are majoring in fields other than math or engineering intermediate algebra is the only prerequisite the book focuses on applications of statistical knowledge rather than the theory behind it the text is named collaborative statistics because students learn best by doing in fact they learn best by working in small groups the old saying two heads are better than one truly applies here our emphasis in this text is on four main concepts · thinking statistically features of connexions[close]
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3 · incorporating technology · working collaboratively · writing thoughtfully these concepts are integral to our course students learn the best by actively participating not by just watching and listening teaching should be highly interactive students need to be thoroughly engaged in the learning process in order to make sense of statistical concepts collaborative statistics provides techniques for students to write across the curriculum to collaborate with their peers to think statistically and to incorporate technology this book takes students step by step the text is interactive therefore students can immediately apply what they read once students have completed the process of problem solving they can tackle interesting and challenging problems relevant to today s world the problems require the students to apply their newly found skills in addition technology ti-83 graphing calculators are highlighted is incorporated throughout the text and the problems as well as in the special group activities and projects the book also contains labs that use real data and practices that lead students step by step through the problem solving process at de anza along with hundreds of other colleges across the country the college audience involves a large number of esl students as well as students from many disciplines the esl students as well as the non-esl students have been especially appreciative of this text they find it extremely readable and understandable collaborative statistics has been used in classes that range from 20 to 120 students and in regular honor and distance learning classes susan dean barbara illowsky[close]
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author ackowledgements 11 we wish to acknowledge the many people who have helped us and have encouraged us in this project at de anza donald rossi and rupinder sekhon and their contagious enthusiasm started us on our path to this book inna grushko and diane mathios painstakingly checked every practice and homework problem inna also wrote the glossary and offered invaluable suggestions kathy plum co-taught with us the first term we introduced the ti-85 lenore desilets charles klein kathy plum janice hector vernon paige carol olmstead and donald rossi of de anza college ann flanigan of kapiolani community college birgit aquilonius of west valley college and terri teegarden of san diego mesa college graciously volunteered to teach out of our early editions janice hector and lenore desilets also contributed problems diane mathios and carol olmstead contributed labs as well in addition diane and kathy have been our sounding boards for new ideas in recent years lisa markus vladimir logvinenko and roberta bloom have contributed valuable suggestions jim lucas and valerie hauber of de anza s office of institutional research along with mary jo kane of health services provided us with a wealth of data we would also like to thank the thousands of students who have used this text so many of them gave us permission to include their outstanding word problems as homework they encouraged us to turn our note packet into this book have offered suggestions and criticisms and keep us going finally we owe much to frank jeffrey and jessica dean and to dan rachel matthew and rebecca illowsky who encouraged us to continue with our work and who had to hear more than their share of i m sorry i can t and just a minute i m working 11 this content is available online at[close]
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