Statistics Success in 20 Minutes a Day

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<ul><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 1/222</p><p>STATISTICSSUCCESS</p><p>in 20 Minutesa Day</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 2/222</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 3/222</p><p>STATISTICSSUCCESSin 20 Minutesa Day</p><p>Linda J.Young</p><p>N E W Y O R K </p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 4/222</p><p>Copyright 2006 LearningExpress, LLC.</p><p>All rights reserved under International and Pan-American Copyright Conventions.</p><p>Published in the United States by LearningExpress, LLC, New York.</p><p>Library of Congress Cataloging-in-Publication Data:</p><p>Young, Linda J., 1952-</p><p>Statistics success in 20 minutes a day / Linda J.Young.</p><p>p. cm.</p><p>Includes bibliographical references.</p><p>ISBN 1-57685-535-X</p><p>1. Mathematical statisticsProblems, exercises, etc. I. Title.</p><p>QA276.2.Y68 2005</p><p>519.5dc22 2005027521</p><p>Printed in the United States of America</p><p>9 8 7 6 5 4 3 2 1</p><p>ISBN 1-57685-535-X</p><p>For information on LearningExpress, other LearningExpress products, or bulk sales, please write to us at:</p><p>LearningExpress</p><p>55 Broadway</p><p>8th Floor</p><p>New York, NY 10006</p><p>Or visit us at:</p><p></p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 5/222</p><p>Linda J. Youngis professor of statistics and director of biostatistics at the University of Florida. She has</p><p>previously served on the faculties at Oklahoma State University and the University of Nebraska.</p><p>About the Author</p><p>v</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 6/222</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 7/222</p><p>Introduction How to Use This Book ix</p><p>Pretest 1Lesson 1 Populations, Samples, and Variables 13</p><p>Lesson 2 Studies 17</p><p>Lesson 3 Describing and Displaying Categorical Data 25</p><p>Lesson 4 Dotplots and Stem-and-Leaf Plots 33</p><p>Lesson 5 Measures of Central Tendency for Numerical Data 41</p><p>Lesson 6 Measures of Dispersion for Numerical Data 47</p><p>Lesson 7 Histograms and Boxplots 55</p><p>Lesson 8 Describing and Displaying Bivariate Data 65</p><p>Lesson 9 Basic Ideas in Probability 73</p><p>Lesson 10 Discrete Probability Distributions 85Lesson 11 Continuous Probability Distributions 91</p><p>Lesson 12 Sampling Distributions and the t-Distribution 101</p><p>Lesson 13 The Law of Large Numbers and the Central Limit Theorem 111</p><p>Lesson 14 Sample Surveys 117</p><p>Lesson 15 Confidence Intervals for Proportions 123</p><p>Lesson 16 Hypothesis Testing for Proportions 129</p><p>Lesson 17 Confidence Intervals and Tests of Hypotheses for Means 137</p><p>Lesson 18 The Matched-Pairs Design and Comparing Two Treatment Means 145</p><p>Lesson 19 Confidence Intervals for Comparing Two Treatment or Population Means 157</p><p>Lesson 20 Analyzing Categorical Data 169Posttest 181</p><p>Answer Key 193</p><p>Appendix How to Prepare for a Test 207</p><p>Contents</p><p>vi i</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 8/222</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 9/222</p><p>Introduction</p><p>ix</p><p>If you have never taken a statistics course, and now find that you need to know the basics of statistics</p><p>this is the book for you. If you have already taken a statistics course, but felt like you never understood</p><p>what the teacher was trying to tell youthis book can teach you what you need to know. If it has been</p><p>a while since you have taken a statistics course, and you need to refresh your skillsthis book will review the</p><p>basics and reteach you the skills you may have forgotten. Whatever your reason for needing to know statis-</p><p>tics, Statistics Success in 20 Minutes a Daywill teach you what you need to know.It gives you the statistics basics</p><p>in clear and straightforward lessons that you can do at your own pace.</p><p> How to Use This Book</p><p>Statistics Success teaches basic concepts in 20 self-paced lessons. The book includes a pretest, a posttest, and</p><p>tips on how to prepare for a standardized test. Before you begin Lesson 1, take the pretest to assess your cur-</p><p>rent statistics abilities. The answer key follows the pretest. This will be helpful in determining your strengths</p><p>and weaknesses. After taking the pretest, move on to Lesson 1.Each lesson offers detailed explanations of a new concept. There are numerous examples with step-by-</p><p>step solutions.As you proceed through a lesson, you will find tips and shortcuts that will help you learn a con-</p><p>cept. Each new concept is followed by a set of practice problems. The answers to the practice problems are</p><p>in the answer key located at the end of the book.</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 10/222</p><p>When you have completed all 20 lessons, take the posttest at the end of the book. The posttest has the</p><p>same format as the pretest, but the questions are different. Compare the results of the posttest with the results</p><p>of the pretest. What are your strengths? Do you have weak areas? Do you need to spend more time on some</p><p>concepts, or are you ready to go to the next level?</p><p> Make a Commitment</p><p>Success does not come without effort. If you truly want to be successful, make a commitment to spend the</p><p>time you need to improve your statistics skills. When you achieve statistics success, you have laid the foun-</p><p>dation for future challenges and opportunities.</p><p>So sharpen your pencil and get ready to begin the pretest!</p><p>INTRODUCTION</p><p>x</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 11/222</p><p>Before you begin Lesson 1, you may want to get an idea of what you know and what you need to learn.</p><p>The pretest will answer some of these questions for you. The pretest consists of 50 multiple-choice</p><p>questions covering the topics in this book. Although 50 questions cant cover every concept, skill, or</p><p>shortcut taught in this book, your performance on the pretest will give you a good indication of your strengths</p><p>and weaknesses. Keep in mind, the pretest does not test all the skills taught in this statistics book.</p><p>If you score high on the pretest, you have a good foundation and should be able to work your way</p><p>through the book quickly. If you score low on the pretest, dont despair. This book will take you through the</p><p>statistics concepts step by step. If you get a low score, you may need to take more than 20 minutes a day to</p><p>work through a lesson. However, this is a self-paced program, so you can spend as much time on a lesson as</p><p>you need. You decide when you fully comprehend the lesson and are ready to go on to the next one.</p><p>Take as much time as you need to do the pretest.You will find that the level of difficulty increases as you</p><p>work your way through the pretest.</p><p>Pretest</p><p>1</p><p>1. a b c d</p><p>2. a b c d</p><p>3. a b c d</p><p>4. a b c d</p><p>5. a b c d</p><p>6. a b c d</p><p>7. a b c d</p><p>8. a b c d</p><p>9. a b c d</p><p>10. a b c d</p><p>11. a b c d</p><p>12. a b c d</p><p>13. a b c d</p><p>14. a b c d</p><p>15. a b c d</p><p>16. a b c d</p><p>17. a b c d</p><p>18. a b c d</p><p>19. a b c d</p><p>20. a b c d</p><p>21. a b c d</p><p>22. a b c d</p><p>23. a b c d</p><p>24. a b c d</p><p>25. a b c d</p><p>26. a b c d27. a b c d</p><p>28. a b c d</p><p>29. a b c d</p><p>30. a b c d</p><p>31. a b c d</p><p>32. a b c d</p><p>33. a b c d</p><p>34. a b c d</p><p>35. a b c d</p><p>36. a b c d</p><p>37. a b c d</p><p>38. a b c d</p><p>39. a b c d</p><p>40. a b c d</p><p>41. a b c d</p><p>42. a b c d</p><p>43. a b c d</p><p>44. a b c d</p><p>45. a b c d</p><p>46. a b c d</p><p>47 a b c d</p><p>48. a b c d</p><p>49. a b c d</p><p>50. a b c d</p><p>AN SW ER SH EE T</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 12/222</p><p> Pretest</p><p>1. The time it takes an employee to drive to work isthe variable of interest. What type of variable is</p><p>being observed?</p><p>a. categorical variable</p><p>b. continuous variable</p><p>c. discrete variable</p><p>d. explanatory variable</p><p>2. A study was conducted to compare two different</p><p>approaches to preparing for an exam. Twenty</p><p>high school students taking chemistry volun-teered to participate. Ten were randomly</p><p>assigned to use the first approach; the other ten</p><p>used the second approach. Each ones perform-</p><p>ance on the next chemistry exam was recorded.</p><p>What type of study is this?</p><p>a. experiment with a broad scope of inference</p><p>b. experiment with a narrow scope of inference</p><p>c. sample survey</p><p>d. observational study</p><p>3. Random digit dialing was used to select house-</p><p>holds in a particular state. An adult in each</p><p>household contacted was asked whether the</p><p>household had adequate health insurance. A</p><p>critic of the poll said that the results were biased</p><p>because households without telephones were not</p><p>included in the survey. As a consequence, the</p><p>estimated percentage of households that had</p><p>adequate health insurance was biased upward.</p><p>What type of bias was the critic concerned</p><p>about?</p><p>a. measurement bias</p><p>b. nonresponse bias</p><p>c. response bias</p><p>d. selection bias</p><p>4. A study was conducted to determine whether a</p><p>newly developed rose smelled better than the</p><p>rose of the standard variety. Twenty students</p><p>were randomly selected from a large high schoolto participate in a smell study. Each selected</p><p>student smelled both roses in a random order</p><p>and selected the one that smelled best. What is</p><p>the population of interest and what are the</p><p>response and explanatory variables?</p><p>a. The population is all students at the large</p><p>high school; the response variable is the rose</p><p>choice; and the explanatory variable is the</p><p>type of rose.</p><p>b. The population is all students at the largehigh school; the response variable is the type</p><p>of rose; and the explanatory variable is the</p><p>rose choice.</p><p>c. The population is all roses of these two types;</p><p>the response variable is the rose choice; and</p><p>the explanatory variable is the type of rose.</p><p>d. The population is all roses of these two types;</p><p>the response variable is the type of rose; and</p><p>the explanatory variable is the rose choice.</p><p>For problems 5 and 6, consider the following 12 data</p><p>points: 10, 12, 10, 18, 16, 15, 9, 14, 11, 13, 12, and 16.</p><p>5. What is the median of these data?</p><p>a. 9</p><p>b. 12</p><p>c. 12.5</p><p>d. 13</p><p>6. What is the interquartile range of these data?</p><p>a. 4</p><p>b. 5</p><p>c. 6</p><p>d. 9</p><p>P R E T E S T</p><p>2</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 13/222</p><p>7. What does the length of the box in a boxplot</p><p>represent?</p><p>a. the range</p><p>b.the interquartile range</p><p>c. the median</p><p>d. the mean</p><p>8. How does one standardize a random variable?</p><p>a. Add the mean.</p><p>b. Subtract the mean.</p><p>c. Add the mean and divide by the standard</p><p>deviation.</p><p>d. Subtract the mean and divide by the standard</p><p>deviation.</p><p>For problems 9 and 10, consider this information: On</p><p>any given day, the probability it will rain is 0.32; the</p><p>probability the wind will blow is 0.2; and the proba-</p><p>bility that it will rain and the wind will blow is 0.1.</p><p>9. For a randomly selected day, what is the proba-</p><p>bility that it will rain or the wind will blow?</p><p>a. 0.42</p><p>b. 0.52c. 0.58</p><p>d. 0.62</p><p>10. For a randomly selected day, what is the proba-</p><p>bility that it will NOT rain and the wind will</p><p>NOT blow?</p><p>a. 0.38</p><p>b. 0.48</p><p>c. 0.58</p><p>d. 0.90</p><p>Use the following information for problems 11, 12,</p><p>and 13. The students in a small high school were sur-</p><p>veyed. Each student was asked whether he or she used</p><p>a safety belt whenever driving. This information andthe gender of the student was recorded as follows:</p><p>11. What is the probability that a randomly selected</p><p>student is a male who does not use his seat belt?</p><p>a.</p><p>b.</p><p>c.</p><p>d.</p><p>12. What is the probability that a randomly selected</p><p>student is a female given that the person is a seat</p><p>belt user?</p><p>a.</p><p>b.</p><p>c.</p><p>d.151205</p><p>82</p><p>205</p><p>82</p><p>151</p><p>82</p><p>105</p><p>54</p><p>205</p><p>31205</p><p>23</p><p>105</p><p>31</p><p>100</p><p>P R E T E S T</p><p>3</p><p>USE OF SAFETY BELTS</p><p>USE SAFETY BELT?</p><p>GENDER YES NO TOTALS</p><p>Female 82 23 105</p><p>Male 69 31 100</p><p>Totals 151 54 205</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 14/222</p><p>13. Is the use of a safety belt independent of gender?</p><p>a. no, because the probability that a randomly</p><p>chosen student is a female does not equal the</p><p>probability of female given safety belt useb. no, because the number of females who use a</p><p>safety belt is not equal to the number of</p><p>males who use a seat belt</p><p>c. yes, because the sample was randomly</p><p>selected</p><p>d. yes, because both genders do use seat belts</p><p>more than they do notuse seat belts</p><p>For problems 14 and 15, consider that 1% of a popu-</p><p>lation has a particular disease. A new test for identify-ing the disease has been developed. If the person has</p><p>the disease, the test is positive 94% of the time. If the</p><p>person does not have the disease,the test is positive 2%</p><p>of the time.</p><p>14. What is the probability that a randomly selected</p><p>person from this population tests positive?</p><p>a. 0.0292</p><p>b. 0.0094</p><p>c. 0.096d. 0.96</p><p>15. A person is randomly selected from this popula-</p><p>tion and tested. She tests positive. Which of the</p><p>following best represents the probability that she</p><p>has the disease?</p><p>a. 0.0094</p><p>b. 0.32</p><p>c. 0.34</p><p>d. 0.94</p><p>Use the following information for problems 16, 17,</p><p>and 18. On any given day, the probability that Megan</p><p>will be late for work is 0.2. Whether or not she is late</p><p>to work is independent from day to day.</p><p>16. Megan was late to work today.What is the</p><p>probability that she will NOT be late to work</p><p>tomorrow?</p><p>a.0.16</p><p>b. 0.2</p><p>c. 0.6</p><p>d. 0.8</p><p>17. Which of the following is closest to the probabil-</p><p>ity that Megan will be late to work at least one of</p><p>the five days next week?</p><p>a. 0.00032</p><p>b. 0.33</p><p>c. 0.41d. 0.67</p><p>18. What is the probability that Megan will be on</p><p>time exactly three days and then be late on the</p><p>fourth one?</p><p>a. 0.0064</p><p>b. 0.1024</p><p>c. 0.16</p><p>d. 0.512</p><p>19. A train is scheduled to leave the station at 3 P.M.</p><p>However, it is equally likely to actually leave the</p><p>station any time from 2:55 to 3:15 P.M. What is</p><p>the probability it will depart the station early?</p><p>a. 0.25</p><p>b. 0.33</p><p>c. 0.67</p><p>d. 0.75</p><p>20. Let zbe a standard normal random variable.</p><p>Find the probability that a randomly selected</p><p>value ofzis between2.1 and 0.4.</p><p>a. 0.1079</p><p>b. 0.3446</p><p>c. 0.5475</p><p>d. 0.6554</p><p>P R E T E S T</p><p>4</p></li><li><p>7/25/2019 Statistics Success in 20 Minutes a Day</p><p> 15/222</p><p>21. Let zbe a standard normal random variable.</p><p>Find z* such that the probability that a randomly</p><p>selected value ofzis greater than z* is 0.2.</p><p>a. 0.84</p><p>b. 0.4207</p><p>c. 0.5793</p><p>d. 0.84</p><p>22. LetXbe a normal random variable with mean</p><p>20 and standard deviation 5.What is the proba-</p><p>bility that a randomly selected value ofXis</p><p>between 15 and 25?</p><p>a. 0.32</p><p>b. 0.68c. 0.95</p><p>d. 0.997</p><p>23. A random sample of size 25 is selected from a</p><p>population that is normally distributed with a</p><p>mean of 15 and a standard deviation of 4. What</p><p>is the sampling distribution of the sample mean?</p><p>a. normal with a mean of 0 and a standard</p><p>deviation of 1</p><p>b. normal with a mean of 15 and a standarddeviation of 0.16</p><p>c. normal with a mean of 15 and a standard</p><p>of 0.8</p><p>d. normal with a mean of 15 and a standard</p><p>deviation of 4</p><p>24. Find t* such that the probability that a randomly</p><p>selected observation from a t-distribution with</p><p>16 degrees of freedom is less than t* is 0.1.</p><p>a. 1.746</p><p>b. 1.337</p><p>c. 1.337</p><p>d. 1.746</p><p>25. A researcher decides to study the bite strength of</p><p>alligators. She believes that if she takes a large</p><p>enough random sample, she will be able to say</p><p>that the average of the bite strengths she recordswill be close to the mean bite strength of all the</p><p>alligators in the population she is studying. Is</p><p>she correct?</p><p>a. No. One can never be sure that the sample</p><p>mean is close to the population mean.</p><p>b. Yes. By the Central Limit Theorem, the sam-</p><p>ple mean will be equal to the population</p><p>mean ifn 30.</p><p>c. Yes. By the Central Limit Theorem, the sam-</p><p>ple mean will be...</p></li></ul>