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Solution Manual for Fundamentals of Statistics, 6th Edition

Solution Manual for Fundamentals of Statistics, 6th Edition simplifies the toughest textbook questions, providing easy-to-follow solutions for every chapter.

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    ’ S S OLUTIONS M ANUAL DIACRI T ECH F UNDAMENTALS OF S TATISTICS : I NFORMED D ECISIONS U SING D ATA S IXTH E DITION Michael Sullivan, III Joliet Junior College

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    Table of Contents Preface Chapter 1 Data Collection 1.1 Introduction to the Practice of Statistics ............................................................................................................. 1 1.2 Observational Studies versus Designed Experiments ......................................................................................... 4 1.3 Simple Random Sampling .................................................................................................................................. 7 1.4 Other Effective Sampling Methods .................................................................................................................... 9 1.5 Bias in Sampling ............................................................................................................................................... 11 1.6 The Design of Experiments .............................................................................................................................. 14 Chapter 1 Review Exercises ........................................................................................................................................ 21 Chapter 1 Test ............................................................................................................................................................. 24 Case Study: Chrysalises for Cash ................................................................................................................................ 26 Chapter 2 Summarizing Data in Tables and Graphs 2.1 Organizing Qualitative Data ............................................................................................................................. 28 2.2 Organizing Quantitative Data ........................................................................................................................... 38 2.3 Graphical Misrepresentations of Data .............................................................................................................. 51 Chapter 2 Review Exercises ........................................................................................................................................ 53 Chapter 2 Test ............................................................................................................................................................. 58 Case Study: The Day the Sky Roared.......................................................................................................................... 62 Chapter 3 Numerically Summarizing Data 3.1 Measures of Central Tendency ......................................................................................................................... 65 3.2 Measures of Dispersion .................................................................................................................................... 72 3.3 Measures of Central Tendency and Dispersion from Grouped Data ................................................................ 89 3.4 Measures of Position and Outliers .................................................................................................................... 99 3.5 The Five-Number Summary and Boxplots ..................................................................................................... 106 Chapter 3 Review Exercises ...................................................................................................................................... 117 Chapter 3 Test ........................................................................................................................................................... 123 Case Study: Who Was “A Mourner”? ....................................................................................................................... 126 Chapter 4 Describing the Relation between Two Variables 4.1 Scatter Diagrams and Correlation ................................................................................................................... 128 4.2 Least-Squares Regression ............................................................................................................................... 149 4.3 The Coefficient of Determination ................................................................................................................... 161 4.4 Contingency Tables and Association .............................................................................................................. 165 Chapter 4 Review Exercises ...................................................................................................................................... 178 Chapter 4 Test ........................................................................................................................................................... 184 Case Study: Thomas Malthus, Population, and Subsistence ..................................................................................... 187 Chapter 5 Probability 5.1 Probability Rules ............................................................................................................................................ 189 5.2 The Addition Rule and Complements............................................................................................................. 198 5.3 Independence and the Multiplication Rule ..................................................................................................... 206 5.4 Conditional Probability and the General Multiplication Rule ........................................................................ 210 5.5 Counting Techniques ...................................................................................................................................... 217 5.6 Simulating Probability Experiments ............................................................................................................... 221 5.7 Putting It Together: Which Method Do I Use? ............................................................................................... 223 Chapter 5 Review Exercises ...................................................................................................................................... 226 Chapter 5 Test ........................................................................................................................................................... 229 Case Study: The Case of the Body in the Bag ........................................................................................................... 230

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    Chapter 6 Discrete Probability Distributions 6.1 Discrete Random Variables............................................................................................................................. 233 6.2 The Binomial Probability Distribution ............................................................................................................ 243 Chapter 6 Review Exercises ...................................................................................................................................... 258 Chapter 6 Test ............................................................................................................................................................ 261 Case Study: The Voyage of the St. Andrew .............................................................................................................. 264 Chapter 7 The Normal Probability Distribution 7.1 Properties of the Normal Distribution ............................................................................................................. 266 7.2 Applications of the Normal Distribution ......................................................................................................... 269 7.3 Assessing Normality ....................................................................................................................................... 289 7.4 The Normal Approximation to the Binomial Probability Distribution ........................................................... 292 Chapter 7 Review Exercises ...................................................................................................................................... 296 Chapter 7 Test ............................................................................................................................................................ 301 Case Study: A Tale of Blood Chemistry.................................................................................................................... 304 Chapter 8 Sampling Distributions 8.1 Distribution of the Sample Mean .................................................................................................................... 306 8.2 Distribution of the Sample Proportion ............................................................................................................ 319 Chapter 8 Review Exercises ...................................................................................................................................... 325 Chapter 8 Test ............................................................................................................................................................ 328 Case Study: Sampling Distribution of the Median .................................................................................................... 330 Chapter 9 Estimating the Value of a Parameter Using Confidence Intervals 9.1 Estimating a Population Proportion ................................................................................................................ 336 9.2 Estimating a Population Mean ........................................................................................................................ 343 9.3 Putting It Together: Which Method Do I Use? ............................................................................................... 353 9.4 Estimating a Population Standard Deviation................................................................................................... 359 9.5 Estimating with Bootstrapping ........................................................................................................................ 361 Chapter 9 Review Exercises ...................................................................................................................................... 366 Chapter 9 Test ............................................................................................................................................................ 370 Case Study: Fire-Safe Cigarettes ............................................................................................................................... 372 Chapter 10 Hypothesis Tests Regarding a Parameter 10.1 The Language of Hypothesis Testing.............................................................................................................. 374 10.2 Hypothesis Tests for a Population Proportion................................................................................................. 377 10.2A Using Simulation to Perform Hypothesis Tests on a Population Proportion .................................................. 388 10.2B Hypothesis Tests for a Population Proportion Using the Normal Model ........................................................ 398 10.3 Hypothesis Tests for a Population Mean......................................................................................................... 408 10.3A Using Simulation and the Bootstrap to Perform Hypothesis Tests on a Population Mean ............................. 419 10.4 Putting It Together: Which Method Do I Use? ............................................................................................... 426 10.5 Hypothesis Tests for a Population Standard Deviation ................................................................................... 430 Chapter 10 Review Exercises .................................................................................................................................... 434 Chapter 10 Test .......................................................................................................................................................... 438 Case Study: How Old Is Stonehenge? ....................................................................................................................... 439

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    Chapter 11 Inference on Two Population Parameters 11.1 Inference about Two Population Proportions ................................................................................................. 442 11.1A Using Randomization Techniques to Compare Two Proportions ................................................................... 457 11.2 Inference about Two Means: Dependent Samples .......................................................................................... 465 11.2A Using Bootstrapping to Conduct Inference on Two Dependent Means.......................................................... 477 11.3 Inference about Two Means: Independent Samples ....................................................................................... 484 11.3A Using Randomization Techniques to Compare Two Independent Means ...................................................... 498 11.4 Putting It Together: Which Method Do I Use? ............................................................................................... 502 11.5 Inference about Two Populations Standard Deviations .................................................................................. 515 Chapter 11 Review Exercises .................................................................................................................................... 520 Chapter 11 Test ......................................................................................................................................................... 525 Case Study: Control in the Design of an Experiment ................................................................................................ 531 Chapter 12 Additional Inferential Methods 12.1 Goodness-of-Fit Test ...................................................................................................................................... 533 12.2 Tests for Independence and the Homogeneity of Proportions ........................................................................ 544 12.3 Testing the Significance of the Least-Squares Regression Model .................................................................. 566 12.3A Using Randomization Techniques on the Slope of the Least-Squares Regression Line ................................. 571 12.4 Confidence and Prediction Intervals ............................................................................................................... 577 Chapter 12 Review Exercises .................................................................................................................................... 583 Chapter 12 Test ......................................................................................................................................................... 590 Case Study: Feeling Lucky? Well, Are You? ............................................................................................................ 597 Appendix B B.1 Lines ............................................................................................................................................................... 600 B.2 Inference about Two Population Proportions: Dependent Samples................................................................ 608 B.3 Comparing Three or More Means (One-Way Analysis of Variance) ............................................................ 611

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    Chapter 1 Data Collection Section 1.1 1. (a) III. Statistics is the science of collecting, organizing, summarizing, and analyzing information in order to draw conclusions and answer questions. It is also about providing a measure of confidence in any conclusions. (b) VIII. The population is the entire group of individuals to be studied. (c) IV. The sample is a subset of the group of individuals that is being studied. (d) VII. The parameter is a numerical summary of a population. (e) I. The statistic is the numerical summary of a sample. (f) VI. The individual is a person or object that is a member of the group being studied. (g) II. Descriptive statistics involves organizing and summarizing data through tables, graphs, and numerical summaries. (h) V. Inferential statistics uses methods that take results from a sample and extends them to the population, and measures the reliability of the result. 2. (a) V. A discrete variable has either a finite number of possible values or countable number of possible values. The values of these variables typically result from counting. (b) IV. Data are information that describe characteristics of an individual. (c) VI. A continuous variable has an infinite number of possible values that are not countable. The values of these variables typically result from measurement. (d) II. A qualitative variable allows for classification of individuals based on some attribute or characteristic. (e) I. A quantitative variable provides numerical measures of individuals. The measures can be added or subtracted, and provide meaningful results. (f) III. A variable is the characteristics of the individuals within the population. 3. 18% is a parameter because it describes a population (all of the governors). 4. 72% is a parameter because it describes a population (the entire class). 5. 32% is a statistic because it describes a sample (the high school students surveyed). 6. 13.3% is a statistic because it describes a sample (the 12th graders surveyed). 7. 0.366 is a parameter because it describes a population (all of Ty Cobb’s at-bats). 8. 43.92 hours is a parameter because it describes a population (all the men who have walked on the moon). 9. 23% is a statistic because it describes a sample (the 6076 adults studied). 10. 44% is a statistic because it describes a sample (the 100 adults interviewed). 11. Qualitative 12. Quantitative 13. Quantitative 14. Qualitative 15. Quantitative 16. Quantitative 17. Qualitative 18. Qualitative 19. Discrete 20. Continuous 21. Continuous 22. Discrete 23. Continuous 24. Continuous 25. Discrete 26. Continuous 27. Nominal 28. Ordinal 29. Ratio 30. Interval 31. Ordinal 32. Nominal 33. Ratio 34. Interval 35. The population consists of all teenagers 13 to 17 years old who live in the United States. The sample consists of the 1028 teenagers 13 to 17 years old who were contacted by the Gallup Organization.

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    2 Chapter 1: Data Collection 36. The population consists of all bottles of Coca- Cola filled by that particular machine on October 15. The sample consists of the 50 bottles of Coca-Cola that were selected by the quality control manager. 37. The population consists of all of the soybean plants in this farmer’s crop. The sample consists of the 100 soybean plants that were selected by the farmer. 38. The population consists of all households within the United States. The sample consists of the 50,000 households that are surveyed by the U.S. Census Bureau. 39. The population consists of all women 27 to 44 years of age with hypertension. The sample consists of the 7373 women 27 to 44 years of age with hypertension who were included in the study. 40. The population consists of all full-time students enrolled at this large community college. The sample consists of the 128 full- time students who were surveyed by the administration. 41. Individuals: Alabama, Colorado, Indiana, North Carolina, Wisconsin. Variables: Minimum age for driver’s license (unrestricted); mandatory belt use seating positions, maximum allowable speed limit (rural interstate) in 2011. Data for minimum age for driver’s license: 17, 17, 18, 16, 18; Data for mandatory belt use seating positions: front, front, all, all, all; Data for maximum allowable speed limit (rural interstate) 2011: 70, 75, 70, 70, 65 (mph.) The variable minimum age for driver’s license is continuous; the variable mandatory belt use seating positions is qualitative; the variable maximum allowable speed limit (rural interstate) 2011 is continuous (although only discrete values are typically chosen for speed limits.) 42. Individuals: 3 Series, 5 Series, 6 Series, 7 Series, X3, Z4 Roadster Variables: Body Style, Weight (lb), Number of Seats Data for body style: Coupe, Sedan, Convertible, Sedan, Sport utility, Coupe; Data for weight: 3362, 4056, 4277, 4564, 4012, 3505 (lb); Data for number of seats: 4, 5, 4, 5, 5, 2. The variable body style is qualitative; the variable weight is continuous; the variable number of seats is discrete. 43. (a) The research objective is to determine if adolescents who smoke have a lower IQ than nonsmokers. (b) The population is all adolescents aged 18–21. The sample consisted of 20,211 18-year-old Israeli military recruits. (c) Descriptive statistics: The average IQ of the smokers was 94, and the average IQ of nonsmokers was 101. (d) The conclusion is that individuals with a lower IQ are more likely to choose to smoke. 44. (a) The research objective is to determine if the application of duct tape is as effective as cryotherapy in the treatment of common warts. (b) The population is all people with warts. The sample consisted of 51 patients with warts. (c) Descriptive statistics: 85% of patients in group 1 and 60% of patients in group 2 had complete resolution of their warts. (d) The conclusion is that duct tape is significantly more effective in treating warts than cryotherapy. 45. (a) The research objective is to determine the proportion of adult Americans who believe the federal government wastes 51 cents or more of every dollar. (b) The population is all adult Americans aged 18 years or older. (c) The sample is the 1017 American adults aged 18 years or older that were surveyed. (d) Descriptive statistics: Of the 1017 individuals surveyed, 35% indicated that 51 cents or more is wasted. (e) From this study, one can infer that many Americans believe the federal government wastes much of the money collected in taxes.

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    Section 1.1: Introduction to the Practice of Statistics 3 46. (a) The research objective is to determine what proportion of adults, aged 18 and over, believe it would be a bad idea to invest $1000 in the stock market. (b) The population is all adults aged 18 and over living in the United States. (c) The sample is the 1018 adults aged 18 and over living in the United States who completed the survey. (d) Descriptive statistics: Of the 1016 adults surveyed, 46% believe it would be a bad idea to invest $1000 in the stock market. (e) The conclusion is that a little fewer than half of the adults in the United States believe investing $1000 in the stock market is a bad idea. 47. (a) State is a qualitative variable because it is an individual categorization. (b) F scale is a qualitative variable because each tornado is rated according to a category. (c) Fatalities is a quantitative variable because it is a numerical measure. It is a discrete variable because it is countable. (d) Length is a quantitative variable because it is a numerical measure. It is a continuous variable because it results from measurement. 48. (a) State is a variable measured at the nominal level because values of the variable name, label, or categorize. In addition, the naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order. (b) F scale is a variable measured at the ordinal level because the naming scheme allows for the values of the variable to be arranged in a ranked or specific order. (c) Fatalities is a variable measured at the ratio level because the ratio of two values makes sense and a value of zero has meaning. (d) Length is a variable measured at the ratio level because the ratio of two values makes sense and a value of zero has meaning. 49. Jersey number is nominal (the numbers generally indicate a type of position played). However, if the researcher feels that lower caliber players received higher numbers, then jersey number would be ordinal since players could be ranked by their number. 50. (a) Nominal; the ticket number is categorized as a winner or a loser. (b) Ordinal; the ticket number gives an indication as to the order of arrival of guests. (c) Ratio; the implication is that the ticket number gives an indication of the number of people attending the party. 51. (a) The research question is to determine if the season of birth affects mood later in life. (b) The sample consisted of the 400 people the researchers studied. (c) The season in which you were born (winter, spring, summer, or fall) is a qualitative variable. (d) According to the article, individuals born in the summer are characterized by rapid, frequent swings between sad and cheerful moods, while those born in the winter are less likely to be irritable. (e) The conclusion was that the season at birth plays a role in one’s temperament. 52. The population is the group to be studied as defined by the research objective. A sample is any subset of the population. 53. Quantitative variables are numerical measures such that meaningful arithmetic operations can be performed on the values of the variable. Qualitative variables describe an attribute or characteristic of the individual that allows researchers to categorize the individual. The values of a discrete random variable result from counting. The values of a continuous random variable result from a measurement. 54. The four levels of measurement of a variable are nominal, ordinal, interval, and ratio. Examples: Nominal—brand of clothing; Ordinal—size of a car (small, mid-size, large); Interval—temperature (in degrees Celsius); Ratio—number of students in a class (Examples will vary.)

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    4 Chapter 1: Data Collection 55. We say data vary, because when we draw a random sample from a population, we do not know which individuals will be included. If we were to take another random sample, we would have different individuals and therefore different data. This variability affects the results of a statistical analysis because the results would differ if a study is repeated. 56. The process of statistics is to (1) identify the research objective, which means to determine what should be studied and what we hope to learn; (2) collect the data needed to answer the research question, which is typically done by taking a random sample from a population; (3) describe the data, which is done by presenting descriptive statistics; and (4) perform inference in which the results are generalized to a larger population. 57. Age could be considered a discrete random variable. A random variable can be discrete by allowing, for example, only whole numbers to be recorded. Section 1.2 1. The response variable is the variable of interest in a research study. An explanatory variable is a variable that affects (or explains) the value of the response variable. In research, we want to see how changes in the value of the explanatory variable affect the value of the response variable. 2. (a) III. A designed experiment is when a researcher randomly assigns the individuals in a study to groups, intentionally manipulates the value of an explanatory variable, controls other explanatory variables at fixed values, and then records the value of the response variable for each individual. (b) V. An observational study is when a researcher measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. That is, the researcher observes the behavior of individuals in the study and records the values of the explanatory and response variables. (c) IV. A lurking variable is an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. In addition, this variable is typically related to other explanatory variables in the study. (d) I. Confounding occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study. (e) II. A confounding variable is an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study. 3. (a) II. A cohort study follows a group of individuals over a long period of time. Characteristics of the individuals are recorded and some individuals will be exposed to certain factors (not intentionally) and others will not. Because the data are collected over time, cohort studies are prospective. (b) III. A cross-sectional study collects information about individuals at a specific point in time, or over a short period of time. (c) I. A case-control study is retrospective, meaning it requires the researcher to look at existing records, or the subject to recall information from the past. Individuals who have certain characteristics are matched with those who don’t. 4. An observational study uses data obtained by studying individuals in a sample without trying to manipulate or influence the variable(s) of interest. In a designed experiment, a treatment is applied to the individuals in a sample in order to isolate the effects of the treatment on a response variable. Only an experiment can establish causation between an explanatory variable and a response variable. Observational studies can indicate a relationship, but cannot establish causation. 5. The choice between an observational study and an experiment depends on the circumstances involved. Sometimes there are ethical reasons why an experiment cannot be conducted. Other times the researcher may conduct an observational study first to validate a belief prior to investing a large amount of time and money into a designed experiment. A designed experiment is preferred if ethics, time, and money are not an issue.

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    Section 1.2: Observational Studies vs. Designed Experiments 5 6. A cohort study identifies the individuals to participate and then follows them over a period of time. During this period, information about the individuals is gathered, but there is no attempt to influence the individuals. Cohort studies are superior to case-control studies because cohort studies do not require recall to obtain the data. 7. There is a perceived benefit to obtaining a flu shot, so there are ethical issues in intentionally denying certain seniors access to the treatment. 8. A retrospective study looks at data from the past either through recall or existing records. A prospective study gathers data over time by following the individuals in the study and recording data as they occur. 9. This is an observational study because the researchers merely observed existing data. There was no attempt by the researchers to manipulate or influence the variable(s) of interest. 10. This is an experiment because the researchers intentionally changed the value of the explanatory variable (medication dose) to observe a potential effect on the response variable (cancer growth). 11. This is an experiment because the explanatory variable (teaching method) was intentionally varied to see how it affected the response variable (score on proficiency test). 12. This is an observational study because no attempt was made to influence the variable of interest. Voting choices were merely observed. 13. This is an observational study because the survey only observed preference of Coke or Pepsi. No attempt was made to manipulate or influence the variable of interest. 14. This is an experiment because the researcher intentionally imposed treatments on individuals in a controlled setting. 15. This is an experiment because the explanatory variable (carpal tunnel treatment regimen) was intentionally manipulated in order to observe potential effects on the response variable (level of pain). 16. This is an observational study because the conservation agents merely observed the fish to determine which were carrying parasites. No attempt was made to manipulate or influence any variable of interest. 17. (a) This is a cohort study because the researchers observed a group of people over a period of time. (b) The response variable is whether the individual has heart disease or not. The explanatory variable is whether the individual is happy or not. (c) There may be confounding due to lurking variables. For example, happy people may be more likely to exercise, which could affect whether they will have heart disease or not. 18. (a) This is a cross-sectional study because the researchers collected information about the individuals at a specific point in time. (b) The response variable is whether the woman has nonmelanoma skin cancer or not. The explanatory variable is the daily amount of caffeinated coffee consumed. (c) It was necessary to account for these variables to avoid confounding with other variables. 19. (a) This is an observational study because the researchers simply administered a questionnaire to obtain their data. No attempt was made to manipulate or influence the variable(s) of interest. This is a cross-sectional study because the researchers are observing participants at a single point in time. (b) The response variable is body mass index. The explanatory variable is whether a TV is in the bedroom or not. (c) Answers will vary. Some lurking variables might be the amount of exercise per week and eating habits. Both of these variables can affect the body mass index of an individual. (d) The researchers attempted to avoid confounding due to other variables by taking into account such variables as “socioeconomic status.” (e) No. Since this was an observational study, we can only say that a television in the bedroom is associated with a higher body mass index.

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    6 Chapter 1: Data Collection 20. (a) This is an observational study because the researchers merely observed the individuals included in the study. No attempt was made to manipulate or influence any variable of interest. This is a cohort study because the researchers identified the individuals to be included in the study, then followed them for a period of time (7 years). (b) The response variable is weight gain. The explanatory variable is whether the individual is married/cohabitating or not. (c) Answers will vary. Some potential lurking variables are eating habits, exercise routine, and whether the individual has children. (d) No. Since this is an observational study, we can only say that being married or cohabitating is associated with weight gain. 21. (a) This is a cross-sectional study because information was collected at a specific point in time (or over a very short period of time). (b) The explanatory variable is delivery scenario (caseload midwifery, standard hospital care, or private obstetric care). (c) The two response variables are (1) cost of delivery, which is quantitative, and (2) type of delivery (vaginal or not), which is qualitative. 22. (a) The explanatory variable is web page design; qualitative (b) The response variables are time on site and amount spent. Both are qualitative. (c) Answers will vary. A confounding variable might be location. Any differences in spending may be due to location rather than to web page design. 23. Answers will vary. This is a prospective, cohort observational study. The response variable is whether the worker had cancer or not, and the explanatory variable is the amount of electromagnetic field exposure. Some possible lurking variables include eating habits, exercise habits, and other health-related variables such as smoking habits. Genetics (family history) could also be a lurking variable. This was an observational study, and not an experiment, so the study only concludes that high electromagnetic field exposure is associated with higher cancer rates. The author reminds us that this is an observational study, so there is no direct control over the variables that may affect cancer rates. He also points out that while we should not simply dismiss such reports, we should consider the results in conjunction with results from future studies. The author concludes by mentioning known ways (based on extensive study) of reducing cancer risks that can currently be done in our lives. 24. (a) This is a cohort study because a group of individuals was identified to participate in the study, and then they were observed over a period of time. (b) Because there is a link established between obesity and cell phone use, and a link between obesity and negative health outcomes, if it is determined that cell- phone users are experiencing higher incidence rates of negative health outcomes, it cannot be established that the factor leading to the negative health outcome is due to the cell phone—it may be due to the lurking variable obesity. 25. Because individuals in the early 1900s were pressured to become right-handed, we would see a lower proportion of left-handers who are older in the study. This would make it seem as though left-handers die younger because the older individuals in the study are primarily right-handed. 26. (a) The research objective is to determine whether lung cancer is associated with exposure to tobacco smoke within the household. (b) This is a case-controlled study because there is a group of individuals with a certain characteristic (lung cancer but never smoked) being compared to a similar group without the characteristic (no lung cancer and never smoked). The study is retrospective because lifetime residential histories were compiled and analyzed. (c) The response variable is whether the individual has lung cancer or not. This is a qualitative variable.

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    Section 1.3: Simple Random Sampling 7 (d) The explanatory variable is the number of “smoker years.” This is a quantitative variable. (e) Answers will vary. Some possible lurking variables are household income, exercise routine, and exposure to tobacco smoke outside the home. (f) The conclusion of the study is that approximately 17% of lung cancer cases among nonsmokers can be attributed to high levels of exposure to tobacco smoke during childhood and adolescence. No, we cannot say that exposure to household tobacco smoke causes lung cancer since this is only an observational study. We can, however, conclude that lung cancer is associated with exposure to tobacco smoke in the home. (g) An experiment involving human subjects is not possible for ethical reasons. Researchers would be able to conduct an experiment using laboratory animals, such as rats. 27. Web scraping can be used to extract data from tables on web pages and then upload the data to a file. Web scraping can also be used to create a data set of words from an online article (that is, fetching unstructured information and transforming it into a structured format through something called parsing and reformatting processes). In addition, web scraping can be used to dynamically call information from websites with links. 28. Answers will vary. Discussions may include the responsibility of host sites to protect private information; the ethics behind using information collected from a site to harm a competitor; the ethics behind putting stress on a host’s servers so that the website slows down; the role of social media to scrape its site for “fake news.” Section 1.3 1. The frame is a list of all the individuals in the population. 2. Simple random sampling occurs when every possible sample of size n has an equally likely chance of occurring. 3. Sampling without replacement means that no individual may be selected more than once as a member of the sample. 4. Random sampling is a technique that uses chance to select individuals from a population to be in a sample. It is used because it maximizes the likelihood that the individuals in the sample are representative of the individuals in the population. In convenience sampling, the individuals in the sample are selected in the quickest and easiest way possible (e.g. the first 20 people to enter a store). Convenience samples likely do not represent the population of interest because chance was not used to select the individuals. 5. Answers will vary. We will use one-digit labels and assign the labels across each row (i.e. Pride and Prejudice – 0, The Sun Also Rises – 1, and so on). In Table I of Appendix A, starting at row 5, column 11, and proceeding downward, we obtain the following labels: 8, 4, 3 In this case, the 3 books in the sample would be As I Lay Dying , A Tale of Two Cities , and Crime and Punishment . Different labeling order, different starting points in Table I in Appendix A, or use of technology will likely yield different samples. 6. Answers will vary. We will use one-digit labels and assign the labels across each row (i.e. Mady – 0, Breanne – 1, and so on). In Table I of Appendix A, starting at row 11, column 6, and then proceeding downward, we obtain the following labels: 1, 5 In this case, the two captains would be Breanne and Payton. Different labeling order, different starting points in Table I in Appendix A, or use of technology will likely yield different results. 7. (a) {616, 630}, {616, 631}, {616, 632}, {616, 645}, {616, 649}, {616, 650}, {630, 631}, {630, 632}, {630, 645}, {630, 649}, {630, 650}, {631, 632}, {631, 645}, {631, 649}, {631, 650}, {632, 645}, {632, 649}, {632, 650}, {645, 649}, {645, 650}, {649, 650} (b) There is a 1 in 21 chance that the pair of courses will be EPR 630 and EPR 645. 8. (a) {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 7}, {3, 4}, {3, 5}, {3, 6}, {3, 7}, {4, 5}, {4, 6}, {4, 7}, {5, 6}, {5, 7}, {6, 7} (b) There is a 1 in 21 chance that the pair The United Nations and Amnesty International will be selected.

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    8 Chapter 1: Data Collection 9. (a) Starting at row 5, column 22, using two- digit numbers, and proceeding downward, we obtain the following values: 83, 94, 67, 84, 38, 22, 96, 24, 36, 36, 58, 34,.... We must disregard 94 and 96 because there are only 87 faculty members in the population. We must also disregard the second 36 because we are sampling without replacement. Thus, the 9 faculty members included in the sample are those numbered 83, 67, 84, 38, 22, 24, 36, 58, and 34. (b) Answers will vary depending on the type of technology used. If using a TI-84 Plus, the sample will be: 4, 20, 52, 5, 24, 87, 67, 86, and 39. Note: We must disregard the second 20 because we are sampling without replacement. 10. (a) Starting at row 11, column 32, using four- digit numbers, and proceeding downward, we obtain the following values: 2869, 5518, 6635, 2182, 8906, 0603, 2654, 2686, 0135, 7783, 4080, 6621, 3774, 7887, 0826, 0916, 3188, 0876, 5418, 0037, 3130, 2882, 0662,…. We must disregard 8906, 7783, and 7887 because there are only 7656 students in the population. Thus, the 20 students included in the sample are those numbered 2869, 5518, 6635, 2182, 0603, 2654, 2686, 0135, 4080, 6621, 3774, 0826, 0916, 3188, 0876, 5418, 0037, 3130, 2882, and 0662. (b) Answers may vary depending on the type of technology used. If using a TI-84 Plus, the sample will be: 6658, 4118, 9, 4828, 3905, 454, 2825, 2381, 495, 4445, 4455, 5759, 5397, 7066, 3404, 6667, 5074, 3777, 3206, 5216. 11. (a) Answers will vary depending on the technology used (including a table of random digits). Using a TI-84 Plus graphing calculator with a seed of 17 and the labels provided, our sample would be North Dakota, Nevada, Tennessee, Wisconsin, Minnesota, Maine, New Hampshire, Florida, Missouri, and Mississippi. (b) Repeating part (a) with a seed of 18, our sample would be Michigan, Massachusetts, Arizona, Minnesota, Maine, Nebraska, Georgia, Iowa, Rhode Island, and Indiana. 12. (a) Answers will vary depending on the technology used (including a table of random digits). Using a TI-84 Plus graphing calculator with a seed of 98 and the labels provided, our sample would be Jefferson, Reagan, Madison, Trump, Pierce, Buchanan, Carter, G. W. Bush. (b) Repeating part (a) with a seed of 99, our sample would be Nixon, Eisenhower, Pierce, Arthur, Trump, Hayes, Clinton, T. Roosevelt.

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    Section 1.4: Other Effective Sampling Methods 9 13. (a) The list provided by the administration serves as the frame. Number each student in the list of registered students, from 1 to 19,935. Generate 25 random numbers, without repetition, between 1 and 19,935 using a random number generator or table. Select the 25 students with these numbers. (b) Answers will vary. 14. (a) The list provided by the mayor serves as the frame. Number each resident in the list supplied by the mayor, from 1 to 5832. Generate 20 random numbers, without repetition, between 1 and 5832 using a random number generator or table. Select the 20 residents with these numbers. (b) Answers will vary. 15. Answers will vary. Members should be numbered 1–32, though other numbering schemes are possible (e.g. 0–31). Using a table of random digits or a random-number generator, four different numbers (labels) should be selected. The names corresponding to these numbers form the sample. 16. Answers will vary. Employees should be numbered 1–29, though other numbering schemes are possible (e.g. 0–28). Using a table of random digits or a random-number generator, four different numbers (labels) should be selected. The names corresponding to these numbers form the sample. 17. Answers will vary. Section 1.4 1. Stratified random sampling may be appropriate if the population of interest can be divided into groups (or strata) that are homogeneous and nonoverlapping. 2. Systematic sampling does not require a frame. 3. Convenience samples are typically selected in a nonrandom manner. This means the results are not likely to represent the population. Convenience samples may also be self- selected, which will frequently result in small portions of the population being overrepresented. 4. Cluster sample 5. Stratified sample 6. False. In a systematic random sample, every k th individual is selected from the population. 7. False. In many cases, other sampling techniques may provide equivalent or more information about the population with less “cost” than simple random sampling. 8. True. When the clusters are heterogeneous, the heterogeneity of each cluster likely resembles the heterogeneity of the population. In such cases, fewer clusters with more individuals from each cluster are preferred. 9. True. Because the individuals in a convenience sample are not selected using chance, it is likely that the sample is not representative of the population. 10. False. With stratified samples, the number of individuals sampled from each strata should be proportional to the size of the strata in the population. 11. Systematic sampling. The quality-control manager is sampling every 8 th chip, starting with the 3 rd chip. 12. Cluster sampling. The commission tests all members of the selected teams (clusters). 13. Cluster sampling. The airline surveys all passengers on selected flights (clusters). 14. Stratified sampling. The congresswoman samples some individuals from each of three different income brackets (strata). 15. Simple random sampling. Each known user of the product has the same chance of being included in the sample. 16. Convenience sampling. The radio station is relying on voluntary response to obtain the sample data. 17. Cluster sampling. The farmer samples all trees within the selected subsections (clusters). 18. Stratified sampling. The school official takes a sample of students from each of the five classes (strata). 19. Convenience sampling. The research firm is relying on voluntary response to obtain the sample data. 20. Systematic sampling. The presider is sampling every 5 th person attending the lecture, starting with the 3 rd person.

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    1 1 0 Chapte 21. Stratified measure intervals 22. Simple r has the s survey. 23. The num selected 66 25 + 216, 241 441, 466 24. Since th but less three-dig Starting Appendi 10 cluste 377, 304 Note tha the table these lab occurren the same 25. Answers number simple r the Repu random different seed for For exam calculato and 40 f selected 14, 4 for the indiv would c and Eng 26. Answers number simple r the emp random different seed for e r 1: Data C d sampling. Sh ements during e s (strata). random sampli same chance of mbers correspon are 16 , 16 2 + 91 = , 91 25 + = 1, 266, 291, 31 6, 491. e number of cl than 1000, we git label betwe at row 8, colum ix A, and proce ers selected are 4, 626, 392, 31 at we discard 8 e because we h bels. We also d nce of 377 beca e cluster twice. s will vary. To the Democrats random sample ublicans 1 to 1 sample of size t starting point each stratum. mple, using a T or with a seed for the Republi would be 6, 9 r the Republica viduals down e onsist of Hayd gler. s will vary. To the managers random sample loyees 1 to 21 sample of size t starting point each stratum. ollection hawn takes a sa each of the fou ng. Each club f being selecte nding to the 20 25 41 = , 41 2 + 116 = , 141, 16 6, 341, 366, 39 lusters is more assign each cl een 001 and 79 mn 38 in Table eeding downw e numbered 76 5, 084, 565, an 22 and 955 in have no clusters discard the seco ause we canno . obtain the sam s 1 to 16 and ob e of size 2. The 6 and obtain a e 2. Be sure to u t in Table I or a TI-84 Plus grap of 38 for the D icans, the numb for the Democ ans. If we had n each column, th dra, Motola, Th obtain the sam 1 to 8 and obta e of size 2. The and obtain a si e 4. Be sure to u t in Table I or a Copyright © 2 ample of ur time member d for the 0 clients 25 66 = , 6, 191, 91, 416, than 100, luster a 5. e I of ward, the 63, 185, nd 508. reading s with ond t select mple, btain a en number simple use a a different phing Democrats bers crats and numbered he sample hompson, mple, ain a en number imple use a a different 2022 Pearson E Fo cal an sel 20 nu the W 27. (a) (b) 28. (a) (b) 29. Sim Str Clu 30. No Th sam Education, Inc. or example, usi lculator with a nd 20 for the em lected would b 0, 3, 11, 9 for th umbered the ind e sample would Weber, Bryant, H ) 4502 50 N n = = ) Randomly s 90. Suppose individuals t 15th, 105th, the 4425th e ) 94503 130 N n = 7269 k = . ) Randomly s 7269. Suppo 2000. Then numbered 2 up to the ind mple Random Number the a table of ra number gen students to s ratified Sample Since class s want to rand students from the sample. uster Sample: Since classe makeup, we select 128 32 = students fro m o . The clusters h is would be c o m pling. . i ng a TI-84 Pl u a seed of 18 fo r m ployees, the n b e 4, 1 for the m h e employees. d ividuals dow n d consist of Li H all, and Gow 90.04 90 = ® ; s elect a numbe r e that we selec t t o be surveye d , 195th, 285th, e mployee on t h 5 7269.5 = ® s elect a numbe r o se that we ra n we will surve y 000, 9269, 16 , d ividual numb e Sample: e students fro m a ndom digits o r n erator to rand o s urvey. e : sizes are simil a d omly select 1 3 m each class t o e s are similar i n e would want t o 4 = classes an d m those class e were not rand o o nsidered con v u s graphing r the managers n umbers m anagers and If we had n each column ndsey, Carlisl e . ; Thus, 90 k = r between 1 a n t 15. Then the d will be the and so on up t h e company li s 7269 ; Thus, r between 1 a n n domly select y the individu a , 538, and so o n e red 939,701. m 1 to 1280. Us r a rando m - o mly select 12 8 a r, we would 28 4 3 2 = o be included i n size and o randomly d include all t h e s in the sampl e omly selected. v enience , e , . n d t o s t. n d a ls n e 8 i n h e e .

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    Section 1.5: Bias in Sampling 11 31. Answers will vary. One design would be a stratified random sample, with two strata being commuters and noncommuters, as these two groups each might be fairly homogeneous in their reactions to the proposal. 32. Answers will vary. One design would be a cluster sample, with classes as the clusters. Randomly select clusters and then survey all the students in the selected classes. However, care would need to be taken to make sure that no one was polled twice. Since this would negate some of the ease of cluster sampling, a simple random sample might be the more suitable design. 33. Answers will vary. One design would be a cluster sample, with the clusters being city blocks. Randomly select city blocks and survey every household in the selected blocks. 34. Answers will vary. One appropriate design would be a systematic sample, after doing a random start, clocking the speed of every tenth car, for example. 35. Answers will vary. Since the company already has a list (frame) of 6600 individuals with high cholesterol, a simple random sample would be an appropriate design. 36. Answers will vary. Since a list of all the households in the population exists, a simple random sample is possible. Number the households from 1 to N , then use a table of random digits or a random-number generator to select the sample. 37. (a) For a political poll, a good frame would be all registered voters who have voted in the past few elections since they are more likely to vote in upcoming elections. (b) Because each individual from the frame has the same chance of being selected, there is a possibility that one group may be over- or underrepresented. (c) By using a stratified sample, the strategist can obtain a simple random sample within each strata (political party) so that the number of individuals in the sample is proportionate to the number of individuals in the population. 38. Random sampling means that the individuals chosen to be in the sample are selected by chance. Random sampling minimizes the chance that one part of the population is over- or underrepresented in the sample. However, it cannot guarantee that the sample will accurately represent the population. 39. Answers will vary. 40. Answers will vary. Section 1.5 1. A closed question is one in which the respondent must choose from a list of prescribed responses. An open question is one in which the respondent is free to choose his or her own response. Closed questions are easier to analyze, but limit the responses. Open questions allow respondents to state exactly how they feel, but are harder to analyze due to the variety of answers and possible misinterpretation of answers. 2. A certain segment of the population is underrepresented if it is represented in the sample in a lower proportion than its size in the population. 3. (a) III. Bias occurs when the results of the sample are not representative of the population. (b) I. Sampling bias occurs when the techniques used to select individuals for a sample favor one part of the population over another. (c) IV. Nonresponse bias occurs when the individuals selected to be in the sample who do not respond to the survey have different opinions from those who do respond. (d) II. Response bias occurs when the answers on a survey do not reflect the true feelings of the respondent. 4. Nonsampling error is the error that results from undercoverage, nonresponse bias, response bias, or data-entry errors. Essentially, it is the error that results from the process of obtaining and recording data. Sampling error is the error that results because a sample is being used to estimate information about a population. Any error that could also occur in a census is considered a nonsampling error. 5. (a) Sampling bias. The survey suffers from undercoverage because the first 60 customers are likely not representative of the entire customer population. (b) Since a complete frame is not possible, systematic random sampling could be used to make the sample more representative of the customer population.

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