Statistics for Business and Economics , 13th Edition Solution Manual

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SOLUTIONSMANUALNANCYBOUDREAUBowling Green UniversitySTATISTICS FORBUSINESSANDECONOMICSTHIRTEENTHEDITIONJames T. McClaveUniversity of FloridaP. George BensonCollege of CharlestonTerry SincichUniversity of South Florida

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Contents1. Statistics, Data, and Statistical Thinking12. Methods for Describing Sets of Data103. Probability944. Random Variables and Probability Distributions1425. Sampling Distributions2476. Inferences Based on a Single Sample: Estimation with Confidence Intervals2827. Inferences Based on a Single Sample: Tests of Hypotheses3328. Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses3989. Design of Experiments and Analysis of Variance48410. Categorical Data Analysis54611. Simple Linear Regression59112. Multiple Regression and Model Building67213. Methods for Quality Improvement: Statistical Process Control79914. Time Series: Descriptive Analyses, Models, and Forecasting86315. Nonparametric Statistics943

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1Chapter 1Statistics, Data, and Statistical Thinking1.1Statistics is a science that deals with the collection, classification, analysis, and interpretation ofinformation or data. It is a meaningful, useful science with a broad, almost limitless scope of applicationsto business, government, and the physical and social sciences.1.2Descriptive statistics utilizes numerical and graphical methods to look for patterns, to summarize, and topresent the information in a set of data. Inferential statistics utilizes sample data to make estimates,decisions, predictions, or other generalizations about a larger set of data.1.3The four elements of a descriptive statistics problem are:1.The population or sample of interest. This is the collection of all the units upon which the variable ismeasured.2.One or more variables that are to be investigated. These are the types of data that are to be collected.3.Tables, graphs, or numerical summary tools. These are tools used to display the characteristic of thesample or population.4.Identification of patterns in the data. These are conclusions drawn from what the summary toolsrevealed about the population or sample.1.4The five elements of an inferential statistical analysis are:1.The population of interest. The population is a set of existing units.2.One or more variables that are to be investigated. A variable is a characteristic or property of anindividual population unit.3.The sample of population units. A sample is a subset of the units of a population.4.The inference about the population based on information contained in the sample. A statisticalinference is an estimate, prediction, or generalization about a population based on informationcontained in a sample.5.A measure of reliability for the inference. The reliability of an inference is how confident one is thatthe inference is correct.1.5The first major method of collecting data is from a published source. These data have already beencollected by someone else and are available in a published source. The second method of collecting data isfrom a designed experiment. These data are collected by a researcher who exerts strict control over theexperimental units in a study. These data are measured directly from the experimental units. The finalmethod of collecting data is observational. These data are collected directly from experimental units bysimply observing the experimental units in their natural environment and recording the values of thedesired characteristics. The most common type of observational study is a survey.1.6Quantitative data are measurements that are recorded on a meaningful numerical scale. Qualitative data aremeasurements that are not numerical in nature; they can only be classified into one of a group of categories.1.7A population is a set of existing units such as people, objects, transactions, or events. A variable is acharacteristic or property of an individual population unit such as height of a person, time of a reflex,amount of a transaction, etc.

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Chapter 121.8A population is a set of existing units such as people, objects, transactions, or events. A sample is a subsetof the units of a population.1.9A representative sample is a sample that exhibits characteristics similar to those possessed by the targetpopulation. A representative sample is essential if inferential statistics is to be applied. If a sample doesnot possess the same characteristics as the target population, then any inferences made using the samplewill be unreliable.1.10An inference without a measure of reliability is nothing more than a guess. A measure of reliabilityseparates statistical inference from fortune telling or guessing. Reliability gives a measure of howconfident one is that the inference is correct.1.11A population is a set of existing units such as people, objects, transactions, or events. A process is a seriesof actions or operations that transform inputs to outputs. A process produces or generates output over time.Examples of processes are assembly lines, oil refineries, and stock prices.1.12Statistical thinking involves applying rational thought processes to critically assess data and inferencesmade from the data. It involves not taking all data and inferences presented at face value, but rathermaking sure the inferences and data are valid.1.13The data consisting of the classifications A, B, C, and D are qualitative. These data are nominal and thusare qualitative. After the data are input as 1, 2, 3, and 4, they are still nominal and thus qualitative. Theonly differences between the two data sets are the names of the categories. The numbers associated withthe four groups are meaningless.1.14Answers will vary. First, number the elements of the population from 1 to 200,000. Using MINITAB,generate 10 numbers on the interval from 1 to 200,000, eliminating any duplicates.The 10 numbers selected for the random sample are:13507589127189226838991123671914961100214485342091198461Elements with the above numbers are selected for the sample.1.15Both the variables current position and type of organization are qualitative. The variable years ofexperience is quantitative.1.16a.The data would represent the population. These data are all of the data that are of interest to theresearchers.b.If the 80 jamming attacks are actually a sample, then the population would be all jamming attacks bythe U.S. military over the past several years.c.The variable “network type” is qualitative.

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Statistics, Data, and Statistical Thinking3d.The variable “number of channels” is qualitative because there are only two categories of possibleresponses.e.If we wanted to measure the number of channels as a quantitative variable, then we would have torecord the exact number of channels for each jamming attack.1.17a.The experimental unit is a firm that had annual balance sheet data from 1973 to 2011 reported onCompustat.b.The variable measured in this study is the DQ value.c.This is an observational study. No variables were manipulated in this study.1.18a.High school GPA is a number usually between 0.0 and 4.0. Therefore, it is quantitative.b.Honors/awards would have responses that name things. Therefore, it would be qualitative.c.The scores on the SAT's are numbers between 200 and 800. Therefore, it is quantitative.d.Gender is either male or female. Therefore, it is qualitative.e.Parent's income is a number: $25,000, $45,000, etc. Therefore, it is quantitative.f.Age is a number: 17, 18, etc. Therefore, it is quantitative.1.19a.The population of interest is all U.S. residents with a listed phone number.b.The variable of interest is the view of each U.S. resident as to whether the president is doing a goodor bad job. It is qualitative.c.The sample is the 2000 individuals selected for the poll.d.The inference of interest is to estimate the proportion of all U.S. residents who believe the presidentis doing a good job.e.The method of data collection is a survey.f.It is not very likely that the sample will be representative of the population of all residents of theUnited States. By selecting phone numbers at random, the sample will be limited to only thosepeople who have telephones. Also, many people share the same phone number, so each personwould not have an equal chance of being contacted. Another possible problem is the time of day thecalls are made. If the calls are made in the evening, those people who work in the evening would notbe represented.1.20a.The population of interest is all professionals who hold ISACA’s Certified Information SecurityManager designation.b.The data-collection method was a survey: 766 responded to the question on whether or not theyexpect to experience a cyberattack against the firm in the coming year. There are possible biasesbecause those who decided to respond to the questionnaire were self-selected. Generally, those whorespond to a questionnaire have very strong opinions, either positive or negative, which may not berepresentative of all those in the population.

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Chapter 14c.The variable measured is whether or not the respondents expect to experience a cyberattack againstthe firm in the coming year.d.Assuming that the sample was representative of the population, we could infer that 82% of allprofessionals who hold ISACA’s Certified Information Security Manager designation expect toexperience a cyberattack against the firm in the coming year.1.21Since the data collected consist of the entire population, this would represent a descriptive study. Flahertyused the data to help describe the condition of the U.S. Treasury in 1861.1.22a.The population of interest is the status of computer crime at all United States businesses andgovernment agencies.b.The method of data collection was a survey. Since not all of those who were sent a surveyresponded, the sample was self-selected. The results are probably not representative of thepopulation. Usually, those who respond to surveys have very strong opinions, either positive ornegative.c.The variable of interest is whether or not the firm or agency had unauthorized use of its computersystems during the year. Since the response would be either yes or no, the variable would bequalitative.d.If the sample was representative, we could infer that approximately 41% of all U. S. corporations andgovernment agencies experienced unauthorized use of their computer systems during the year.1.23a.This is a designed experiment because the college students were randomly assigned to a group.b.The experimental unit is a college student.c.The two variables are type of condition and type of disposal. Both type of condition and type ofdisposal are qualitative.d.We could infer that in the population of all college students, those who could be placed in theusefulness is salientcondition will recycle at a much higher rate (68%) than those who could beplaced in thecontrolcondition (37%).1.24a.The experimental unit of interest is a college student.b.Both the variables street crossing performance score and memory task score are quantitativevariables.c.This is an application of inferential statistics. Data were collected from a sample of students andconclusions were made about the entire population based on the information found in the sample.1.25a.The experimental unit for this study is a single-family residential property in Arlington, Texas.b.The variables measured are the sale price and the Zillow estimated value. Both of these variables arequantitative.c.If these 2,045 properties were all the single-family residential properties sold in Arlington, Texas inthe past 6 months, then this would be considered the population.d.If these 2,045 properties represent a sample, then the population would be all the singe-familyresidential properties sold in the last 6 months in Arlington, Texas.

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Statistics, Data, and Statistical Thinking5e.No. The real estate market across the United States varies greatly. The prices of single-familyresidential properties in this small area are probably not representative of all properties across theUnited States.1.26a.The experimental unit for this study is an NFL quarterback.b.The variables measured in this study include draft position, NFL winning ratio, and QB productionscore. Since the draft position was put into 3 categories, it is a qualitative variable. The NFL winningratio and the QB production score are both quantitative.c.Since we want to project the performance of future NFL QBs , this would be an application ofinferential statistics.1.27a.The population of interest is all individuals who took GMAT in the time period.b.The method of data collection was a survey.c.This is probably not a representative sample. The sample was self-selected. Not all of those whowere selected for the study responded to all four surveys. Those who did respond to all 4 surveysprobably have very strong opinions, either positive or negative, which may not be representative ofall of those in the population.1.28a.The population of interest is all CPA firms.b.A survey was used to collect the data.c.This sample was probably not representative. Not all of those selected to be in the sample responded.In fact, only 992 of the 23,500 people who were sent the survey responded. Generally, those who dorespond to surveys have very strong opinions, either positive or negative. These may not be theopinions of all CPA firms.d.Since the sample may not be representative, the inferences drawn in the study may not be valid.1.29a.Length of maximum span can take on values such as 15 feet, 50 feet, 75 feet, etc. Therefore, it isquantitative.b.The number of vehicle lanes can take on values such as 2, 4, etc. Therefore, it is quantitative.c.The answer to this item is "yes" or "no," which is not numeric. Therefore, it is qualitative.d.Average daily traffic could take on values such as 150 vehicles, 3,579 vehicles, 53,295 vehicles, etc.Therefore, it is quantitative.e.Condition can take on values "good," "fair," or "poor," which are not numeric. Therefore, it isqualitative.f.The length of the bypass or detour could take on values such as 1 mile, 4 miles, etc. Therefore, it isquantitative.g.Route type can take on values "interstate," U.S.," "state," "county," or "city," which are not numeric.Therefore, it is qualitative.1.30a.The variable of interest to the researchers is the rating of highway bridges.

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Chapter 16b.Since the rating of a bridge can be categorized as one of three possible values, it is qualitative.c.The data set analyzed is a population since all highway bridges in the U.S. were categorized.d.The data were collected observationally. Each bridge was observed in its natural setting.1.31a.The process being studied is the distribution of pipes, valves, and fittings to the refining, chemical,and petrochemical industries by the Wallace Company of Houston.b.The variables of interest are the speed of the deliveries, the accuracy of the invoices, and the qualityof the packaging of the products.c.The sampling plan was to monitor a subset of current customers by sending out a questionnaire twicea year and asking the customers to rate the speed of the deliveries, the accuracy of the invoices, andthe quality of the packaging minutes. The sample is the total numbers of questionnaires received.d.The Wallace Company's immediate interest is learning about the delivery process of its distributionof pipes, valves, and fittings. To do this, it is measuring the speed of deliveries, the accuracy of theinvoices, and the quality of its packaging from the sample of its customers to make an inferenceabout the delivery process to all customers. In particular, it might use the mean speed of its deliveriesto the sampled customers to estimate the mean speed of its deliveries to all its customers. It mightuse the mean accuracy of its invoices from the sampled customers to estimate the mean accuracy ofits invoices of all its customers. It might use the mean rating of the quality of its packaging from thesampled customers to estimate the mean rating of the quality of its packaging of all its customers.e.Several factors might affect the reliability of the inferences. One factor is the set of customersselected to receive the survey. If this set is not representative of all the customers, the wronginferences could be made. Also, the set of customers returning the surveys may not be representativeof all its customers. Again, this could influence the reliability of the inferences made.1.32a.The population of interest would be the set of all students. The sample of interest would be thestudents participating in the experiment. The variable measured in this study is whether the studentwould spend money on repairing a very old car or not.b.The data-collection method used was a designed experiment. The students participating in theexperiment were randomly assigned to one of three emotional states and then asked a question.c.The researcher could estimate the proportion of all students in each of the three emotional states whowould spend money to repair a very old car.d.One factor that might affect the reliability of the inference drawn are whether the students in theexperiment were representative of all students. It is stated that the sample was made up of volunteerstudents. Chances are that these volunteer students were not representative of all students. Inaddition, if these students were all from the same school, they probably would not be representativeof the population of students either.1.33a.The population of interest would be all accounting alumni of a large southwestern university.b.Age would produce quantitative data – the responses would be numbers.Gender would produce qualitative data – the responses would be ‘male’ or ‘female’.Level of education would produce qualitative data – the responses could be categories such collegedegree, masters’ degree, or PhD degree.

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Statistics, Data, and Statistical Thinking7Income would produce quantitative data – the responses would be numbers.Job satisfaction score would produce quantitative data. We would assume that a satisfaction scorewould be a number, where the higher the number, the higher the job satisfaction.Machiavellian rating score would produce quantitative data. We would assume that a rating scorewould be a number, where the higher the score, the higher the Machiavellian traits.c.The sample is the 198 people who returned the useable questionnaires.d.The data collection method used was a survey.e.The inference made by the researcher is that Machiavellian behavior is not required to achievesuccess in the accounting profession.f.Generally, those who respond to surveys are those with strong feelings (in either direction) toward thesubject matter. Those who do not have strong feelings for the subject matter tend not to answersurveys. Those who did not respond might be those who are not real happy with their jobs or thosewho are not real unhappy with their jobs. Thus, we might have no idea what type of scores thesepeople would have on the Machiavellian rating score.1.34a.The experimental units for this study are engaged couples who used a particular website.b.There are two variables of interest – the price of the engagement ring and the level of appreciation.Price of the engagement ring is a quantitative variable because it is measured on a numerical scale.Level of appreciation is a qualitative variable. There are 7 different categories for this variable thatare then assigned numbers.c.The population of interest would be all engaged couples.d.No, the sample is probably not representative. Only engaged couples who used a particular web sitewere eligible to be in the sample. Then, only those with “average” American names were invited tobe in the sample.e.Answers will vary. First, we will number the individuals from 1 to 50. Using MINITAB, 25 randomnumbers were generated on the interval from 1 to 50. The random numbers are:1, 4, 5, 8, 12, 13, 17, 18, 19, 20, 22, 26, 27, 30, 31, 33, 34, 35, 38, 39, 40, 42, 43, 46, 49The individuals who were assigned the numbers corresponding to the above numbers would beassigned to one role and the remaining individuals would be assigned to the other role.1.35a.Some possible questions are:1.In your opinion, why has the banking industry consolidated in the past few years? Check allthat apply.a.Too many small banks with not enough capital.b.A result of the Savings and Loan scandals.c.To eliminate duplicated resources in the upper management positions.d.To provide more efficient service to the customers.e.To provide a more complete list of financial opportunities for the customers.f.Other. Please list.

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Chapter 182.Using a scale from 1 to 5, where 1 means strongly disagree and 5 means strongly agree,indicate your agreement to the following statement: "The trend of consolidation in the bankingindustry will continue in the next five years."1 strongly disagree2 disagree3 no opinion4 agree5 strongly agreeb.The population of interest is the set of all bank presidents in the United States.c.It would be extremely difficult and costly to obtain information from all bank presidents. Thus, itwould be more efficient to sample just 200 bank presidents. However, by sending the questionnairesto only 200 bank presidents, one risks getting the results from a sample which is not representative ofthe population. The sample must be chosen in such a way that the results will be representative of theentire population of bank presidents in order to be of any use.1.36Answers will vary. Using MINITAB, the 5 seven-digit phone numbers generated with area code 373 were:373-639-0598373-411-9164373-502-7699373-782-2719373-930-32311.37a.The population of interest is the set of all people in the United States over 14 years of age.b.The variable being measured is the employment status of each person. This variable is qualitative.Each person is either employed or not.c.The problem of interest to the Census Bureau is inferential. Based on the information contained inthe sample, the Census Bureau wants to estimate the percentage of all people in the labor force whoare unemployed.1.38a.The process being studied is the process of filling beverage cans with softdrink at CCSB's Wakefieldplant.b.The variable of interest is the amount of carbon dioxide added to each can of beverage.c.The sampling plan was to monitor five filled cans every 15 minutes. The sample is the total numberof cans selected.d.The company's immediate interest is learning about the process of filling beverage cans withsoftdrink at CCSB's Wakefield plant. To do this, they are measuring the amount of carbon dioxideadded to a can of beverage to make an inference about the process of filling beverage cans. Inparticular, they might use the mean amount of carbon dioxide added to the sampled cans of beverageto estimate the mean amount of carbon dioxide added to all the cans on the process line.e.The technician would then be dealing with a population. The cans of beverage have already beenprocessed. He/she is now interested in the outputs.1.39Suppose we want to select 900 intersections by numbering the intersections from 1 to 500,000. We wouldthen use a random number table or a random number generator from a software program to select 900distinct intersection points. These would then be the sampled markets.Now, suppose we want to select the 900 intersections by selecting a row from the 500 and a column fromthe 1,000. We would first number the rows from 1 to 500 and number the columns from 1 to 1,000.Using

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Statistics, Data, and Statistical Thinking9a random number generator, we would generate a sample of 900 from the 500 rows. Obviously, many rowswill be selected more than once. At the same time, we use a random number generator to select 900columns from the 1,000 columns. Again, some of the columns could be selected more than once. Placingthese two sets of random numbers side-by-side, we would use the row-column combinations to select theintersections. For example, suppose the first row selected was 453 and the first column selected was 731.The first intersection selected would be row 453, column 731. This process would be continued until 900unique intersections were selected.1.40Answers will vary.a.The results as stated indicate that by eating oat bran, one can improve his/her health. However, theonly way to get the stated benefit is to eat only oat bran with limited results. People may change theireating habits expecting an outcome that is almost impossible.b.In order to investigate the impact of domestic violence on birth defects, one would need to collectdata on all kinds of birth defects and whether the mother suffered any domestic violence or not duringher pregnancy. One could use an observational study survey to collect the data.c.Very few people arealwayshappy with the way they are. However, many people are happy withthemselves most of the time. One might want to ask a series of questions to measure self-esteemrather than just one. One question might ask what percent of the time the high school girl is happywith the way she is.d.The results of the study are probably misleading because of the fact that if someone relied on alimited number of foods to feed her children it does not imply that the children are hungry. Inaddition, one might cut the size of a meal because the children were overweight, not because therewas not enough food. One might get better information about the proportion of hungry Americanchildren by actually recording what a large, representative sample of children eat in a week.e.A leading question gives information that seems to be true, but may not be complete. Based on theincomplete information, the respondent may come to a different decision than if the information wasnot provided.

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10Chapter 2Methods for Describing Sets of Data2.1First, we find the frequency of the grade A. The sum of the frequencies for all five grades must be 200.Therefore, subtract the sum of the frequencies of the other four grades from 200. The frequency for gradeA is:200(36 + 90 + 30 + 28) = 200184 = 16To find the relative frequency for each grade, divide the frequency by the total sample size, 200. Therelative frequency for the grade B is 36/200 = .18. The rest of the relative frequencies are found in asimilar manner and appear in the table:Grade on Statistics ExamFrequencyRelative FrequencyA: 9010016.08B: 808936.18C: 657990.45D: 506430.15F: Below 5028.14Total2001.002.2a.To find the frequency for each class, count the number of times each letter occurs. The frequenciesfor the three classes are:ClassFrequencyX8Y9Z3Total20b.The relative frequency for each class is found by dividing the frequency by the total sample size. Therelative frequency for the class X is 8/20 = .40. The relative frequency for the class Y is 9/20 = .45.The relative frequency for the class Z is 3/20 = .15.ClassFrequencyRelative FrequencyX8.40Y9.45Z3.15Total201.00

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Methods for Describing Sets of Data11c.The frequency bar chart is:C la s sFrequencyZYX9876543210d.The pie chart for the frequency distribution is:2.3a.107.615174Upb.57.328174Spc.10.057174Rpd..615 360221.4,.328 360118.1,.057 36020.5XYZCategory15.0%Z45.0%Y40.0%XPie Chart of Class

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12Chapter 2e.Using MINITAB, the pie chart is:f.61.5% of the STEM participants are from urban areas, 32.8% are from suburban areas, and 5.7% arefrom rural areas.g.Using MINITAB, the bar chart is:Both charts give the same information.2.4a.According to the pie chart, .760 of the sample currently have.a cable/satellite TV subscription athome. The total number of adults sampled who have a cable/satellite TV subscription at home is1,5211803002,001. The proportion is1,521.7602,001.UrbanSuburbanRuralCategory5.7%Rural32.8%Suburban61.5%UrbanPie Chart of LocationRuralSuburbanUrban706050403020100LocPercentPercent is calculated within all data.

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