Data problem solving.

Mathematics

Kenyattta university

Question Description

Hello, This a problem I need you to solve easy and simple and few It wont take more than an hour. I will provide for you the book and everything you need.

In class work #1 January 26th

1. Power Point ch 1 Slide #8 in power point first four categories draw a pie and bar graph.

2. Power Point ch 1 Slide #11 make a histogram of the data

3. Power Point ch 1 Slide #11 make a stemplot of the data

HOMEWORK #1 January 26th

In Book

1.1 a,b

1.3 a,b,c

1.5

1.9a,b

pleas do it by computer not hand written




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FM.indd Page xxv 11/9/11 3:58:39 PM user-s163 user-F452 FM.indd Page i 11/10/11 3:45:17 PM user-s163 user-F452 The Basic Practice of Statistics SIXTH EDITION D AV I D S . M O O R E Purdue University WILLIAM I. NOTZ The Ohio State University MICHAEL A. FLIGNER The Ohio State University W. H. Freeman and Company New York FM.indd Page ii 11/9/11 3:58:32 PM user-s163 Publisher: Ruth Baruth Acquisitions Editor: Karen Carson Executive Marketing Manager: Jennifer Somerville Developmental Editors: Andrew Sylvester and Leslie Lahr Senior Media Acquisitions Editor: Roland Cheyney Senior Media Editor: Laura Capuano Associate Editor: Katrina Wilhelm Assistant Media Editor: Catriona Kaplan Editorial Assistant: Tyler Holzer Photo Editor: Cecilia Varas Photo Researcher: Elyse Rieder Cover and Text Designer: Blake Logan Senior Project Editor: Mary Louise Byrd Illustrations: Macmillan Solutions Production Coordinator: Susan Wein Composition: Aptara®, Inc. Printing and Binding: Quad Graphics Library of Congress Control Number: 2011934674 Student Edition (Hardcover w/cd) Student Edition (Paperback w/cd) Student Edition (Looseleaf w/cd) ISBN-13: 978-1-4641-0254-7 ISBN-13: 978-1-4641-0434-3 ISBN-13: 978-1-4641-0433-6 ISBN-10: 1-4641-0254-6 ISBN-10: 1-4641-0434-4 ISBN-10: 1-4641-0433-6 © 2013, 2010, 2007, 2004 by W. H. Freeman and Company All rights reserved Printed in the United States of America First printing W. H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com user-F452 FM.indd Page iii 11/18/11 11:54:13 PM user-s163 user-F452 Brief Contents Pa r t I 1 Exploring Data Exploring Data: Variables and Distributions CHAPTER 1 Picturing Distributions with Graphs 3 CHAPTER 2 Pa r t I I I Describing Distributions with Numbers 39 Quantitative Response Variable Inference about a Population Mean 437 Two-Sample Problems 465 Categorical Response Variable CHAPTER 20 Inference about a Population Proportion 493 The Normal Distributions 69 Exploring Data: Relationships CHAPTER 4 Scatterplots and Correlation 97 CHAPTER 19 CHAPTER 5 Regression 125 CHAPTER 6 Two-Way Tables* CHAPTER 7 Exploring Data: Part I Review Pa r t I I From Exploration to Inference 197 159 175 CHAPTER 21 Comparing Two Proportions CHAPTER 22 Inference about Variables: Part III Review 533 Pa r t I V Inference about Relationships Producing Data Producing Data: Sampling 199 Producing Data: Experiments Commentary: Data Ethics* Probability and Sampling Distributions 246 CHAPTER 10 Introducing Probability 259 CHAPTER 9 435 CHAPTER 18 CHAPTER 3 CHAPTER 8 Inference about Variables Sampling Distributions 285 CHAPTER 12 General Rules of Probability* 307 Binomial Distributions* 331 Foundations of Inference CHAPTER 14 Confidence Intervals: The Basics 351 CHAPTER 15 Tests of Significance: The Basics 369 CHAPTER 16 Inference in Practice CHAPTER 17 From Exploration to Inference: Part II Review 417 551 CHAPTER 23 Two Categorical Variables: The Chi-Square Test 553 CHAPTER 24 Inference for Regression CHAPTER 25 One-Way Analysis of Variance: Comparing Several Means 623 Pa r t V Optional Companion Chapters 223 CHAPTER 11 515 CHAPTER 13 587 (available on the BPS CD and online) 391 CHAPTER 26 Nonparametrics Tests 26-3 CHAPTER 27 Statistical Process Control CHAPTER 28 Multiple Regression* CHAPTER 29 More about Analysis of Variance 29-3 27-3 28-3 *Starred material is not required for later parts of the text. iii FM.indd Page iv 11/9/11 3:58:32 PM user-s163 user-F452 Detailed Table of Contents To the Instructor viii Media and Supplements xix About the Authors xxiv To the Student xxvi Pa r t I CHAPTER 4 Scatterplots and Correlation 1 Exploring Data CHAPTER 1 Picturing Distributions with Graphs 3 Individuals and variables 3 Categorical variables: pie charts and bar graphs Quantitative variables: histograms 11 Interpreting histograms 15 Quantitative variables: stemplots 20 Time plots 23 6 Measuring center: the mean 40 Measuring center: the median 41 Comparing the mean and the median 42 Measuring spread: the quartiles 43 The five-number summary and boxplots 45 Spotting suspected outliers* 48 Measuring spread: the standard deviation 49 Choosing measures of center and spread 51 Using technology 53 Organizing a statistical problem 55 Regression lines 125 The least-squares regression line 128 Using technology 130 Facts about least-squares regression 132 Residuals 135 Influential observations 139 Cautions about correlation and regression 142 Association does not imply causation 144 CHAPTER 6 Two-Way Tables* 159 Marginal distributions 160 Conditional distributions 162 Simpson’s paradox 166 CHAPTER 7 Exploring Data: Part I Review Part I summary 177 Test yourself 180 Supplementary exercises 175 191 69 Density curves 69 Describing density curves 73 Normal distributions 75 The 68–95–99.7 rule 77 The standard Normal distribution 80 Finding Normal proportions 81 Using the standard Normal table 83 Finding a value given a proportion 86 *Starred material is not required for later parts of the text. iv Explanatory and response variables 97 Displaying relationships: scatterplots 99 Interpreting scatterplots 101 Adding categorical variables to scatterplots 104 Measuring linear association: correlation 106 Facts about correlation 108 CHAPTER 5 Regression 125 CHAPTER 2 Describing Distributions with Numbers 39 CHAPTER 3 The Normal Distributions 97 Pa r t I I From Exploration to Inference CHAPTER 8 Producing Data: Sampling 199 Population versus sample 199 How to sample badly 202 Simple random samples 203 197 FM.indd Page v 11/9/11 3:58:32 PM user-s163 user-F452 • Inference about the population 208 Other sampling designs 209 Cautions about sample surveys 210 The impact of technology 213 CHAPTER 9 Producing Data: Experiments CHAPTER 13 Binomial Distributions* 232 351 The reasoning of tests of significance 370 Stating hypotheses 372 P-value and statistical significance 374 Tests for a population mean 378 Significance from a table* 382 253 CHAPTER 16 Inference in Practice 391 Conditions for inference in practice 392 Cautions about confidence intervals 395 Cautions about significance tests 397 Planning studies: sample size for confidence intervals 401 Planning studies: the power of a statistical test* 402 268 CHAPTER 11 Sampling Distributions 285 Parameters and statistics 285 Statistical estimation and the law of large numbers Sampling distributions 290 _ The sampling distribution of x 293 The central limit theorem 295 CHAPTER 12 General Rules of Probability* CHAPTER 14 Confidence Intervals: The Basics CHAPTER 15 Tests of Significance: The Basics 369 259 The idea of probability 260 The search for randomness* 262 Probability models 264 Probability rules 266 Finite and discrete probability models Continuous probability models 271 Random variables 275 Personal probability* 276 331 The reasoning of statistical estimation 352 Margin of error and confidence level 354 Confidence intervals for a population mean 357 How confidence intervals behave 361 Commentary: Data Ethics* 246 Institutional review boards 248 Informed consent 248 Confidentiality 250 Clinical trials 252 Behavioral and social science experiments v The binomial setting and binomial distributions 331 Binomial distributions in statistical sampling 333 Binomial probabilities 334 Using technology 336 Binomial mean and standard deviation 338 The Normal approximation to binomial distributions 340 223 Observation versus experiment 223 Subjects, factors, treatments 225 How to experiment badly 228 Randomized comparative experiments 229 The logic of randomized comparative experiments Cautions about experimentation 234 Matched pairs and other block designs 236 CHAPTER 10 Introducing Probability D E T A I L E D T A BL E O F CON TE N TS 287 Part II summary 419 Test yourself 423 Supplementary exercises Pa r t I I I 307 Independence and the multiplication rule The general addition rule 312 Conditional probability 314 The general multiplication rule 316 Independence again 318 Tree diagrams 318 CHAPTER 17 From Exploration to Inference: Part II Review 431 Inference about 435 Variables 308 417 CHAPTER 18 Inference about a Population Mean 437 Conditions for inference about a mean 437 The t distributions 438 The one-sample t confidence interval 440 FM.indd Page vi 11/18/11 11:53:50 PM user-s163 vi user-F452 DETA ILED TA B LE O F CO N T E N T S The one-sample t test 443 Using technology 446 Matched pairs t procedures 449 Robustness of t procedures 452 The chi-square test statistic 560 Cell counts required for the chi-square test 561 Using technology 562 Uses of the chi-square test 567 The chi-square distributions 570 The chi-square test for goodness of fit* 572 CHAPTER 19 Two-Sample Problems 465 CHAPTER 24 Inference for Regression Two-sample problems 465 Comparing two population means 466 Two-sample t procedures 469 Using technology 474 Robustness again 477 Details of the t approximation* 480 Avoid the pooled two-sample t procedures* 481 Avoid inference about standard deviations* 482 CHAPTER 25 One-Way Analysis of Variance: Comparing Several Means 623 The sample proportion p̂ 494 Large-sample confidence intervals for a proportion 496 Accurate confidence intervals for a proportion 499 Choosing the sample size 502 Significance tests for a proportion 504 Comparing several means 625 The analysis of variance F test 625 Using technology 628 The idea of analysis of variance 631 Conditions for ANOVA 633 F distributions and degrees of freedom Some details of ANOVA* 640 515 Two-sample problems: proportions 515 The sampling distribution of a difference between proportions 516 Large-sample confidence intervals for comparing proportions 517 Using technology 518 Accurate confidence intervals for comparing proportions Significance tests for comparing proportions 522 Notes and Data Sources Tables 520 CHAPTER 22 Inference about Variables: Part III Review 533 Part III summary 536 Test yourself 538 Supplementary exercises 587 Conditions for regression inference 589 Estimating the parameters 590 Using technology 593 Testing the hypothesis of no linear relationship 597 Testing lack of correlation 598 Confidence intervals for the regression slope 600 Inference about prediction 602 Checking the conditions for inference 607 CHAPTER 20 Inference about a Population Proportion 493 CHAPTER 21 Comparing Two Proportions • 655 675 TABLE A TABLE B TABLE C TABLE D TABLE E Standard Normal probabilities 676 Random digits 678 t distribution critical values 679 Chi-square distribution critical values 680 Critical values of the correlation r 681 Answers to Selected Exercises Index 545 Inference about Relationships CHAPTER 23 Two Categorical Variables: The Chi-Square Test 553 Two-way tables 553 The problem of multiple comparisons 556 Expected counts in two-way tables 558 551 682 733 Pa r t V Pa r t I V 637 Optional Companion Chapters (available on the BPS CD and online) CHAPTER 26 Nonparametric Tests 26-3 Comparing two samples: the Wilcoxon rank sum test The Normal approximation for W 26-8 26-4 FM.indd Page vii 11/9/11 3:58:32 PM user-s163 user-F452 • Using technology 26-10 What hypotheses does Wilcoxon test? 26-13 Dealing with ties in rank tests 26-14 Matched pairs: the Wilcoxon signed rank test 26-19 The Normal approximation for W ⫹ 26-22 Dealing with ties in the signed rank test 26-24 Comparing several samples: the Kruskal-Wallis test 26-27 Hypotheses and conditions for the Kruskal-Wallis test 26-29 The Kruskal-Wallis test statistic 26-29 CHAPTER 27 Statistical Process Control 27-3 Processes 27-4 Describing processes 27-4 The _ idea of statistical process control 27-9 x charts for process monitoring 27-10 s charts for process monitoring 27-16 Using control charts 27-23 Setting up control charts 27-25 Comments on statistical control 27-32 Don’t confuse control with capability! 27-34 Control charts for sample proportions 27-36 Control limits for p charts 27-37 D E T A I L E D T A BL E O F CON TE N TS CHAPTER 28 Multiple Regression* 28-3 Parallel regression lines 28-4 Estimating parameters 28-8 Using technology 28-13 Inference for multiple regression 28-16 Interaction 28-26 The multiple linear regression model 28-32 The woes of regression coefficients 28-39 A case study for multiple regression 28-41 Inference for regression parameters 28-53 Checking the conditions for inference 28-58 CHAPTER 29 More about Analysis of Variance 29-3 Beyond one-way ANOVA 29-3 Follow-up analysis: Tukey pairwise multiple comparisons 29-8 Follow-up analysis: contrasts* 29-12 Two-way ANOVA: conditions, main effects, and interaction 29-16 Inference for two-way ANOVA 29-23 Some details of two-way ANOVA* 29-32 vii FM.indd Page viii 11/9/11 3:58:33 PM user-s163 user-F452 To the Instructor: About this Book elcome to the sixth edition of The Basic Practice of Statistics. This book is the cumulation of 40 years of teaching undergraduates and 20 years of writing texts. Previous editions have been very successful, and we think that this new edition is the best yet. In this preface we describe for instructors the nature and features of the book and the changes in this sixth edition. BPS is designed to be accessible to college and university students with limited quantitative background—“just algebra” in the sense of being able to read and use simple equations. It is usable with almost any level of technology for calculating and graphing—from a $15 “two-variable statistics” calculator through a graphing calculator or spreadsheet program through full statistical software. Of course, graphs and calculations are less tedious with good technology, so we recommend making available to students the most effective technology that circumstances permit. Despite its rather low mathematical level, BPS is a “serious” text in the sense that it wants students to do more than master the mechanics of statistical calculations and graphs. Even quite basic statistics is very useful in many fields of study and in everyday life, but only if the student has learned to move from a real-world setting to choose and carry out statistical methods and then carry conclusions back to the original setting. These translations require some conceptual understanding of such issues as the distinction between data analysis and inference, the critical role of where the data come from, the reasoning of inference, and the conditions under which we can trust the conclusions of inference. BPS tries to teach both the mechanics and the concepts needed for practical statistical work, at a level appropriate for beginners. BPS is designed to reflect the actual practice of statistics, where data analysis and design of data production join with probability-based inference to form a coherent science of data. There are good pedagogical reasons for beginning with data analysis (Chapters 1 to 7), then moving to data production (Chapters 8 and 9), and then to probability (Chapters 10 to 13) and inference (Chapters 14 to 29). In studying data analysis, students learn useful skills immediately and get over some of their fear of statistics. Data analysis is a necessary preliminary to inference in practice, because inference requires clean data. Designed data production is the surest foundation for inference, and the deliberate use of chance in random sampling and randomized comparative experiments motivates the study of probability in a course that emphasizes data-oriented statistics. BPS gives a full presentation of basic probability and inference (20 of the 29 chapters) but places it in the context of statistics as a whole. W GUIDING PRINCIPLES AND THE GAISE GUIDELINES David Moore has based BPS on three principles: balanced content, experience with data, and the importance of ideas. These principles are widely accepted by statisticians concerned about teaching and are directly connected to and reflected by the viii FM.indd Page ix 11/9/11 3:58:33 PM user-s163 user-F452 • T O T H E I N STRUC TOR themes of the College Report of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Project. The GAISE Guidelines includes six recommendations for the introductory statistics course. The content, coverage, and features of BPS are closely aligned to these recommendations: 1. Emphasize statistical literacy and develop statistical thinking. The intent of BPS is to be modern and accessible. The exposition is straightforward and concentrates on major ideas and skills. One principle of writing for beginners is not to try to tell students everything you know. Another principle is to offer frequent stopping points, marking off digestible bites of material. Statistical literacy is promoted throughout BPS in the many examples and exercises drawn from the popular press and from many fields of study. Statistical thinking is promoted in examples and exercises that give enough background to allow students to consider the meaning of their calculations. Exercises often ask for conclusions that are more than a number (or “reject H0”). Some exercises require judgment in addition to right-or-wrong calculations and conclusions. Statistics, more than mathematics, depends on judgment for effective use. BPS begins to develop students’ judgment about statistical studies. 2. Use real data. The study of statistics is supposed to help students work with data in their varied academic disciplines and in their unpredictable later employment. Students learn to work with data by working with data. BPS is full of data from many fields of study and from everyday life. Data are more than mere numbers—they are numbers with a context that should play a role in making sense of the numbers and in stating conclusions. Examples and exercises in BPS, though intended for beginners, use real data and give enough background to allow students to consider the meaning of their calculations. 3. Stress conceptual understanding rather than mere knowledge of procedures. A first course in statistics introduces many skills, from making a stemplot and calculating a correlation to choosing and carrying out a significance test. In practice (even if not always in the course), calculations and graphs are automated. Moreover, anyone who makes serious use of statistics will need some specific procedures not taught in her college stat course. BPS therefore tries to make clear the larger patterns and big ideas of statistics, not in the abstract, but in the context of learning specific skills and working with specific data. Many of the big ideas are summarized in graphical outlines. Three of the most useful appear inside the front cover. Formulas without guiding principles do students little good once the final exam is past, so it is worth the time to slow down a bit and explain the ideas. 4. Foster active learning in the classroom. Fostering active learning is the business of the teacher, though an emphasis on working with data helps. To this end, we have created interactive applets to our specifications and made them available online and on the text CD. The applets are designed primarily to help in learning statistics rather than in doing statistics. An icon calls ix FM.indd Page x 11/9/11 3:58:33 PM user-s163 x user-F452 TO THE INS TR U CTO R • attention to comments and exercises based on the applets. We suggest using selected applets for classroom demonstrations even if you do not ask students to work with them. The Correlation and Regression, Confidence Interval, and P-value applets, for example, convey core ideas more clearly than any amount of chalk and talk. We also provide Web exercises at the end of each chapter. Our intent is to take advantage of the fact that most undergraduates are “Web savvy.” These exercise ...
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