Solution Manual for Business Statistics, Global Edition, 10th Edition

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SOLUTIONSMANUALBUSINESSSTATISTICSADECISION-MAKINGAPPROACHTENTHEDITIONDavid F. GroebnerBoise State UniversityPatrick W. ShannonBoise State UniversityPhillip C. FryBoise State University

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iiiContentsChapter 1The Where, Why, and How of Data Collection1Section 1.11Section 1.23Section 1.35Section 1.48End of Chapter Exercises8Chapter 2Graphs, Charts, and Tables—Describing Your Data11Section 2.111Section 2.228Section 2.343End of Chapter Exercises53Chapter 3Describing Data Using Numerical Measures63Section 3.163Section 3.276Section 3.386End of Chapter Exercises94Chapter 4Introduction to Probability113Section 4.1113Section 4.2121End of Chapter Exercises134Chapter 4 Questions139Chapter 5Discrete Probability Distributions145Section 5.1145Section 5.2155Section 5.3166End of Chapter Exercises173Chapter 6Introduction to Continuous Probability Distributions181Section 6.1181Business Application187Section 6.2196End of Chapter Exercises201Chapter 7Introduction to Sampling Distributions209Section 7.1209Section 7.2218Section 7.3228End of Chapter Exercises240Chapter 8Estimating Single Population Parameters249Section 8.1249Section 8.2262Section 8.3271End of Chapter Exercises280

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ivChapter 9Introduction to Hypothesis Testing285Section 9.1285Computer Database Exercises289Section 9.2291Section 9.3299End of Chapter Exercises309Chapter 10Estimation and Hypothesis Testing for Two Population Parameters319Section 10.1319Section 10.2326Section 10.3335Section 10.4344End of Chapter Exercises350Chapter 11Hypothesis Tests and Estimation for Population Variances357Section 11.1357Section 11.2365End of Chapter Exercises368Chapter 12Analysis of Variance373Section 12.1373Section 12.2385Section 12.3396End of Chapter Exercises406Chapter 13Goodness-of-Fit Tests and Contingency Analysis417Section 13.1417Section 13.2425End of Chapter Exercises437Business Applications438Chapter 14Introduction to Linear Regression and Correlation Analysis445Section 14.1445Section 14.2455Section 14.3471End of Chapter Exercises481Chapter 15Multiple Regression Analysis and Model Building491Section 15.1491Section 15.2499Section 15.3506Section 15.4521Section 15.5530End of Chapter Exercises548Chapter 16Analyzing and Forecasting Time-Series Data569Section 16.1569Section 16.2572Database Exercises590Section 16.3595Business Applications599End of Chapter Exercises607

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vChapter 17Introduction to Nonparametric Statistics629Section 17.1629Section 17.2634Section 17.3645End of Chapter Exercises650Chapter 18Introducing Business Analytics659Section 18.1659Chapter 19Introduction to Decision Analysis (Online)669Section 19.1669Business Applications671Section 19.2Skill Development677Business Applications678Section 19.3Business Applications680End of Chapter ExercisesBusiness Applications684Chapter 20Introduction to Quality and Statistical Process Control (Online)695Section 20.1695End of Chapter Exercises710

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1Chapter 1: The Where, Why, and How of Data CollectionSection 1.11.1.This application is primarily descriptive in nature. The owner wishes to develop a presentation.She will most likely use charts, graphs, tables and numerical measures to describe her data.1.2.The graph is a bar chart. A bar chart displays values associated with categories. In this case thecategories are the departments at the food store. The values are the total monthly sales (indollars) in each department. A bar chart also typically has gaps between the bars. A histogramhas no gaps and the horizontal axis represents the possible values for a numerical variable.1.3.A bar chart is used whenever you want to display data that has already been categorized while ahistogram is used to display data over a range of values for the factor under consideration.Another fundamental difference is that there typically are gaps between the bars on a bar chart butthere are no gaps between the bars of a histogram.1.4.Businesses often make claims about their products that can be tested using hypothesis testing.For example, it is not enough for a pharmaceutical company to claim that its new drug is effectivein treating a disease. In order for the drug to be approved by the Food and Drug Administrationthe company must present sufficient evidence that the drug first does no harm and that it alsoprovides an effective treatment against the disease. The claims that the drug does no harm and isan effective treatment can be tested using hypothesis testing.1.5.The company could use statistical inference to determine if its parts last longer. Because it is notpossible to examine every part that could be produced the company could examine a randomlychosen subset of its parts and compare the average life of the subset to the average life of arandomly chosen subset of the competitor’s parts. By using statistical inference procedures thecompany could reach a conclusion about whether its parts last longer or not.1.6.Student answers will vary depending on the periodical selected and the periodical's issue date, butshould all address the three parts of the question.

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2Business Statistics: A Decision-Making Approach,Tenth Edition1.7.The appropriate chart in this case is a histogram where the horizontal axis contains the number ofmissed days and the height of the bars represent the number of employees who missed eachnumber of daysHistogram: Missed Days for Illness or Injury0204060801001201401601800-2 days3-5 days6-8 days8-10 daysDays MissedNumber of EmployeesNote, there are no gaps between the bars.1.8.Because it would be too costly, too time consuming, or practically impossible to contact everysubscriber to ascertain the desired information, the decision makers atFortunemight decide touse statistical inference, particularly estimation, to answer its questions. By looking at a subset ofthe data and using the procedures of estimation it would be possible for the decision makers toarrive at values for average age and average income that are within tolerable limits of the actualvalues.1.9.Student answers will vary depending on the business periodical or newspaper selected and thearticle referenced. Some representative examples might include estimates of the number ofCEO's who will vote for a particular candidate, estimates of the percentage increase in wages forfactory workers, estimates of the average dollar advertising expenditures for pharmaceuticalcompanies in a specific year, and the expected increase in R&D expenditures for the comingquarter.1.10.Student answers will vary. However, the examples should illustrate how statistics has been usedand should clearly indicate the type of statistical analysis employed.

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Chapter 1: The Where, Why, and How of Data Collection3Section 1.21.11.As discussed in this section, the pet store would most likely use a written survey or a telephonesurvey to collect the customer satisfaction data.1.12.A leading question is one that is designed to elicit a specific response, or one that might influencethe respondent’s answer by its wording. The question is posed so that the respondent believes theresearcher has a specific answer in mind when the question is asked, or worded in such a way thatthe respondent feels obliged to provide an answer consistent with the question. For example, aquestion such as “Do you agree with the experts who recommend that more tax dollars be givento clean up dangerous and unhealthy pollution?” could cause respondents to provide the answerthat they think will be consistent with the “experts” with whom they do not want to disagree.Leading question should be avoided in surveys because they may introduce bias.1.13.An experiment is any process that generates data as its outcome. The plan for performing theexperiment in which the variable of interest is defined is referred to as an experimental design. Inthe experimental design one or more factors are identified to be changed so that the impact on thevariable of interest can be observed or measured.1.14.There will likely by a high rate of nonresponse bias since many people who work days will not behome during the 9–11 AM time slot. Also, the data collectors need to be careful where they getthe phone number list as some people do not have listed phones in phone books and others haveno phone or only a cell phone. This may result in selection bias.1.15.a.Observation would be the most likely method. Observers could be located at various bikeroutes and observe the number of riders with and without helmets. This would likely bebetter than asking people if they wear a helmet since the popular response might be to say yeseven when they don’t always do so.b.A telephone survey to gas stations in the state. This could be a cost effective way of gettingdata from across the state. The respondent would have the information and be able to providethe correct price.c.A written survey of passengers. This could be given out on the plane before the plane landsand passengers could drop the surveys in a box as they de-plane. This method would likelygarner higher response rates compared to sending the survey to passengers’ mailing addressand asking them to return the completed survey by mail.1.16.The two types of validity mentioned in the section are internal validity and external validity. Forthis problem external validity is easiest to address. It simply means the sampling method chosenwill be sufficient to insure the results based on the sample will be able to be generalized to thepopulation of all students. Internal validity would involve making sure the data gatheringmethod, for instance a questionnaire, accurately determines the respondent’s attitude toward theregistration process.1.17.This data could have been collected through a survey. Employees of the USDA could provideperiodic reports of fire ant activity in their region. Also, medical reports could be used to collectdata assuming people with bites had required medical attention.1.18.There are many potential sources of bias associated with data collection. If data is to be collectedusing personal interviews it will be important that the interviewer be trained so that interviewerbias, arising from the way survey questions are asked, is not injected into the survey. If thesurvey is conducted using either a mail survey or a telephone survey then it is important to beaware of nonresponse bias from those who do not respond to the mailing or refuse to answer your

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4Business Statistics: A Decision-Making Approach,Tenth Editioncalls. You must also be careful when selecting your survey subjects so that selection bias is not aproblem. In order to have useful, reliable data that is representative of the true student opinionsregarding campus food service, it is necessary that the data collection process be conducted in amanner that reduces or eliminates the potential for these and other sources of potential bias.1.19.For retailers technology that scans the product UPC code at checkout makes the collection of datafast and accurate. Retailers that use such technology can automatically update their inventoryrecords and develop an extensive collection of customer buying habits. By applying advancedstatistical techniques to the data the retailer can identify relationships among purchases that mightotherwise go unnoticed. Such information could enable retailers to target their advertising oreven rearrange the placement of products in the store to increase sales. Manufacturing firms usebar code scanning to collect information concerning product availability and product quality.Credit card purchases are automatically tracked by the retailer and the bankcard company. In thisway the credit card company is able to track your purchases and even alert you to potential fraudif purchases on your card appear to be unusual. Finally, some companies are using radiofrequency identification (RFID) to track products through their supply chain, so that productdelays and inventory problems can be minimized.1.20.One advantage of this form of data gathering is the same as for mail questionnaires. That is lowcost. Additional factors being speed of delivery and, with current software, with closed- endedquestions, instant updating of data analysis. Disadvantages are also similar, in particular lowresponse and potential confusion about questions. An additional factor might be the ability ofcompetitors to “hack” into the database and analysis program.1.21.Student answers will vary. Look for clarity of questions and to see that the issue questions aredesigned to gather useful data. Look for appropriate demographic questions.1.22.Students should select some form of personal observation as the data-gathering technique. Inaddition, there should be a discussion of a sampling procedure with an effort made to ensure thesample randomly selected both days of the week unless daily observations are made, andrandomly selected times of the day since 24 hour observation would likely be impossible. Acomplete answer would also address efforts to reduce the potential bias of having an observerstanding in an obvious manner by the displays.1.23.Student answers will vary. However, the issue questions should be designed to gather the desireddata regarding customers’ preferences for the use of the space. Demographic questions shouldprovide data so that the responses can be broken down appropriately so that United Fitness Centermanagers can determine which subset of customers have what opinion about this issue.Regarding questionnaire layout, look at neatness and answer location space. Make sure questionsare properly worded, used reasonable vocabulary, and are not leading questions.1.24.The results of the survey are based on telephone interviews with 744 adults, aged 18 and older.Students may also answer that the survey could have been conducted using a written survey viamail questionnaire or internet survey. Because telephone interviews were used to collect thesurvey data nonresponse biases associated with sampled adults who are not at home whenphoned, or adults who refuse to participate in the survey. There is also the problem that someadults do not have a landline phone. If written surveys are used to collect the data then it isimportant to guard against nonresponse bias from those sampled adults who do not complete thesurvey There is also the problem of selection bias. In phone interviews we may miss the peoplewho work evenings and nights. If written surveys are used we must be careful to select arepresentative sample of the adult population.

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Chapter 1: The Where, Why, and How of Data Collection5Section 1.31.25.a.Because the population is spread over a large geographical area, a cluster random samplecould be selected to reduce travel costs.b.A stratified random sample would probably be used to keep sample size as small as possible.c.Most likely a convenience sample would be used since doing a statistical sample would betoo difficult.1.26.To determine the range of employee numbers for the first employee selected in a systematicrandom sample use the following:Population Size18,000Part Range180Sample Size100Thus, the first person selected will come from employees 1–180. Once that person is randomlyselected, the second person will be the one numbered 180 higher than the first, and so on.1.27.Whenever a descriptive numerical measure such as an average is calculated from the entirepopulation it is a parameter. The corresponding measure calculated from a subset of thepopulation, that is to say a sample, is a statistic.1.28.Statistical sampling techniques consist of those sampling methods that select samples based onchance. Nonstatistical sampling techniques consist of those methods of selecting samples usingconvenience, judgment, or other nonchance processes. In convenience sampling, samples arechosen because they are easy or convenient to sample. There is no attempt to randomize theselection of the selected items. In convenience sampling not every item in the population has arandom chance of being selected. Rather, items are sampled based on their convenience alone.Thus, convenience sampling is not a statistical sampling method.1.29.From a numbered list of all customers who own a certificate of deposit the bank would need torandomly determine a starting point between 1 andk, wherekwould be equal to25000/1000 = 25. This could be done using a random number table or by having a statisticalpackage or a spreadsheet generate a random number between 1 and 25. Once this value isdetermined the bank would select that numbered customer as the first sampled customer and thenselect every 25th customer after that until 100 customers are sampled.1.30.A census is an enumeration of the entire set of measurements taken from the population as awhole. While in some cases, the items of interest are obtained from people such as through asurvey, in many instances the items of interest come from a product or other inanimate object.For example, a study could be conducted to determine the defect rate for items made on aproduction line. The census would consist of all items produced on the line in a defined period oftime.1.31.Values computed from a sample are always considered statistics. In order for a value, such as anaverage, to be considered a parameter it must be computed from all items in the population.1.32.In stratified random sampling, the population is divided into homogeneous groups called strata.The idea is to make all items in a stratum as much alike as possible with respect to the variable ofinterest thereby reducing the number of items that will need to be sampled from each stratum. Incluster sampling, the idea is to break the population into heterogeneous groups called clusters(usually on a geographical basis) such that each cluster looks as much like the original population

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6Business Statistics: A Decision-Making Approach,Tenth Editionas possible. Then clusters are randomly selected and from the cluster, individual items areselected using a statistical sampling method.1.33.Using Excel, choose the Data tab, select Data Analysis from the Analysis Group , then RandomNumber Generation—shown as follows:The next step is to complete the random number generation dialog as follows:The resulting random numbers generated are:

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Chapter 1: The Where, Why, and How of Data Collection7Note, the students’ answers may differ since Excel generates different streams of randomnumbers each time it is used. Also, if the application requires integer numbers, the DecreaseDecimal option can be used.1.34.If these percentages were based on all students attending college in those years they would beparameters, if the percentages were based on a sample they would be statistics.1.35.This is a statistic. A poll would be a sample of eligible voters rather than all eligible voters.1.36.Solutiona.Stratified random samplingb.Simple random sampling or possibly cluster random samplingc.Systematic random samplingd.Stratified random sampling1.37.This is a statistical sample. Every employee has an equal chance of being selected using thismethod. In fact, this is an example of a simple random sample because every possible sample ofsize 50 has an equal chance of being selected.1.38.a.Student answers will varyb.Cluster sampling could be used to ensure that you get all types of cereal. Make each clusterthe area where certain cereals are located (i.e., isle, row, shelf, etc.)c.Cluster sampling would give you a better idea of the inventory of all types of cereal. Simplerandom sampling could possibly end up with only looking at 2 or 3 cereal types.1.39.Students should choose the Data tab, select Data Analysis from the Analysis group—RandomNumber Generation process. Students’ answers will differ since Excel generates differentstreams of random numbers each time it is used, but 40 random numbers should be generatedfrom a uniform distribution with values ranging from 1 to 578. Since the application requiresinteger numbers, the Decrease Decimal option should be used.1.40.a.The population should be all users of cross-country ski lots and trailheads in Colorado.b.Several sampling techniques could be selected. Be sure that some method of ensuringrandomness is discussed. In addition, some students might give greater weight to frequentusers of the lots. In which case the population would really be user days rather thanindividual users.c.Students using Excel should choose the Data tab, select Data Analysis from the Analysisgroup—Random Number Generation process. Students’ answers may differ since Excelgenerates different streams of random numbers each time it is used. Since the applicationrequires integer numbers, the Decrease Decimal option should be used.1.41.a.Since there are 4,000 patient files we could give each file a unique identification numberconsisting of 4 digits. The first file would be given the identification number “0001.” Thelast file would be given the identification number of “4000.” By assigning each patient anumber and randomly selecting the 100 numbers allows each possible sample of 100 an equalchance of being selected.b.Either use a random number table (randomly select the starting row and column), or use acomputer program, such as Microsoft Excel, which has a random number generator.c.Since each patient is assigned a 4-digit identification number, we would need a 4-digitrandom number for each random number selected.d.Answers will vary.

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8Business Statistics: A Decision-Making Approach,Tenth EditionSection 1.41.42.a.Time-seriesb.Cross-sectionalc.Time-seriesd.Cross-sectional1.43.Qualitative data are categories or numerical values that represent categories. Quantitative data isdata that is purely numerical.1.44.a.Ordinal—categories with defined orderb.Nominal—categories with no defined orderc.Ratiod.Nominal—categories with no defined order1.45.Nominal data involves placing observations in separate categories according to some measurablecharacteristic. Ordinal data also involves placing observations into separate categories, but thecategories can be rank-ordered.1.46.Since the circles involve a ranking from best to worst, this would be ordinal data.1.47.a.The data are cross-sectional. The data are collected from 2,300 customers at approximatelythe same point in timeb.This is a ratio level, quantitative variable. The data represent a measurement of time.c.Ordinal with a numerical value representing customers rating of level of service1.48.a.Nominal Datab.Ratio Datac.Ratio Datad.Ratio Datae.Nominal1.49.a.Cross-sectionalb.Time-seriesc.Cross-sectionald.Cross-sectionale.Time-Series1.50.Columns A–G are nominal—they are all codesColumns H–L are ratio level.End of Chapter Exercises1.51.Answers will vary with the student. But a good discussion should include the following factors:Sampling techniques and possible problems selecting a representative sample.Determining how to develop questions to measure approval.Structuring questions to avoid bias.The measurement scale associated with the questions.The fact these polls tend to develop time-series data.

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Chapter 1: The Where, Why, and How of Data Collection91.52.Nominal data or ordinal data.1.53.Interval or ratio data.1.54.Ratings are typical uses of ordinal scale data. And since ratings are based on personal opinion,even though people are using the same scale, a direct comparison between the two ratings is notpossible. This is a common problem when people are asked to rate an object using an ordinalscale.1.55.Answers will vary with the student. But a good discussion should include the following factors:Sampling techniques and possible problems selecting a representative sample.Determining how to measure confidence.Structuring questions to avoid bias.The measurement scale associated with the questions.The fact this poll is specifically intended to develop time-series data.1.56.Answers will vary with the student.1.57.Answers will vary with the student.1.58.a.No because a random sample means that every item in the population has an equal chance ofbeing selected. Individuals who do not have or use email do not have an equal chance ofbeing included in this survey. Also, volunteer emails would not be random.b.In this survey the biggest drawback is that only individuals with strong feelings one way orthe other are apt to respond to this survey. This could lead to a great deal of bias in theresults of the survey. Another big problem with a survey is nonresponse bais. Again becausethey are requesting viewers to write in there will be a great deal of nonresponse to thissurvey. I would also include in the answer that the question being asked is somewhat leading.The phrase “using too much force in routine traffic stops” implies that, in fact, force is beingused which one would not expect in a routine traffic stop.1.59.a.They would probably want to sample the salsa jars as they come off the assembly line at theplant for a specified time period. They would want to use a random sample. One methodwould be to take a systematic random sample. They could then calculate the percentage ofthe sample that had an unacceptable thickness.b.The product is going to be ruined after testing it. You would not want to ruin the entireproduct that comes off the assembly line.1.60.a.Student answers will vary but one method would be personal observation at grocery stores oranother method would be to simply look at their sales. Are buyers of the energy drinkspurchasing bottles or cans?b.If using personal observation just have people at grocery stores observe people over aspecified period of time and note which are selecting cans and which are selecting bottles andlook at the percentages of each.c.You would be looking at ratio data because you could have a true 0 if, for example, no onepurchased bottles.d.Depends on the way the data are collected. Sales data would be quantitative.

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10Business Statistics: A Decision-Making Approach,Tenth Edition1.61.a.The fact that the friend has selected his favorite players means that all players did not have achance of being selected in the sample. The sample would be biased toward the type ofplayers the friend favors.b.One method would be to obtain a list of all NBA players. Then assign each player a number.Then you could use Excel’s random number generator to obtain a random sample of 40players from the list.1.62.The appropriate design would be a stratified random sampling method. Start by dividing thestudents into class standing (Freshman, Sophomore, Junior, and Senior). Then randomly selectstudents from each strata.

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