Introduction to Business Statistics, 7th Edition Solution Manual

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1CHAPTER 1A PREVIEW OF BUSINESS STATISTICSSECTION EXERCISES1.1d/p/e In ancient times, statistics was mainly employed for counting people or possessions in order tofacilitate taxation.1.2d/p/m Statistical methods are useful in all facets of business today. Statistics can be used to describeinformation, to analyze data, to reach conclusions, and to make decisions.1.3d/p/m Descriptive statistics are used to summarize and describe a set of data. Inferential statistics areused to make generalizations, estimates, forecasts, or other judgments about the population from whichthe data (sample) is taken. Inferential statistics are involved when a state senator surveys some of herconstituents in order to obtain guidance on how she should vote. She is using statistics to make judgmentsabout the populationbased on the datafrom the sample.1.4d/p/m This represents descriptive statistics; we are summarizing and describing the data.1.5d/p/m This information represents inferential statistics since we are using information collected from asample of 20 adults to make inferences about all adults.1.6d/p/e Qualitative variables or "attributes" involve counting the number of people or objects that fallwithin categories. Quantitative variables determine how much of something is possessed.1.7d/p/e Discrete quantitative variables cantake on onlycertain values along an interval, with the valueshaving gaps between them. Discrete variables are applicable when we want to count the number of timessomething occurs. Continuous quantitative variables can take on any value along an interval. Continuousvariables are applicable when there are no gaps between the exact values which these variables can takeon, such as weight, height, volume, or distance.Note: In this solutions manual, exercises are categorized according to type, tools required, and level ofdifficulty:Type:Tools:Difficulty:d = definitional/conceptualp = pencile = easyc = computationala = calculatorm = moderatep = problemc = computerd = difficultFor example, "c/a/m" refers to an exercise that is computational in nature, requires a pocket calculator,and is judged to be moderate in difficulty. The classifications are of necessity subjective. We haveattempted to specify the most basic tool that could be practical for the task. In some cases (e.g., simpleregression), the pocket calculator can be used even though a computer statistical package (if available)is preferred. In other cases (e.g., multiple regression and analysis of variance), the computer isautomatically specified as the required tool.1.8d/p/m

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2a.This information might be interpreted as a qualitative variable if we view it asexpressing that theschool is among those which have been accredited for the past 15 years versus those which have notbeen accredited for the past 15 years.b.This information might be interpreted as a quantitative variable if we view it as counting the number ofyears the school has been accredited during the past 15-year period. For other locksmithing schoolsover the past 15 years, the number of years they have been accredited could be any integer value from0 to 15.1.9d/p/ma.This information is on the ordinal scale. The industries are viewed in terms of rank instead of thedistance between them. However, we do not have a unit of measurement to describe how many morestrikes Industry A has than Industry B.b.This information is on the ratio scale. The industries can be viewed in terms of rank (C has lost fewerdays per worker), and thereis a unit of measurement enabling us to describe how many more daysIndustry D has lost per worker.Also, there is an absolute zero point and multiplesare meaningful.1.10d/p/ma.The lodge might give each guest a number to identifythestatein whichheorsheresides.b.The lodge could rank the rooms at the lodge frommost attractive to least attractive.c.The lodge could describe different months of the year according to their average temperatures.d.The lodge could record the number of skiers at the lodge from each one of the New England states.1.11d/p/m The restaurant might be able to make decisionspertaining to such matters asthe quality offood,the courtesy and number of employees,and the cleanliness of the restaurant.1.12d/p/m The company might report the percentage of burglaries in homes with their product versus thepercentage in homes without their product. Hopefully, the former percentage is lower than the latter.1.13d/p/m The company may manipulate the data to show what it wants to show; for example, bydistorting the scale on a graph to make a large deficit appear very small. Another possibility is to use asample that is not representative of the population.1.14d/p/e You should ask yourself what benefits the person or company stands to gain from theconclusions reached by the study.CHAPTER EXERCISES1.15d/p/m This information would represent inferential statistics, since a sample is used to makegeneralizations about the population.1.16d/p/ma.Qualitative; you are in one category or the other.b.Qualitative; you are in one category or the other.c.Quantitative, discrete; the number of people that attended is countable (0, 1, 2, …).d.Quantitative, discrete; the price can take on only certain values along an interval.e.Quantitative, continuous; time can take on a value at any point along an interval.f.Quantitative, discrete; the number of students that belong to a fraternity or sorority is countable.1.17d/p/m The amount of money paid out in premiums and the number of policies purchased in theprevious year would play a role in how much you pay for your policy. Data such as the number of

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3accidents, speeding tickets, or other moving violations you've had in the past few years could also play arole, as could data regarding accident or claim frequencies associated with the type of vehicle you drive.1.18d/p/ma.Ratio scale; there is an absolute zero point associated with the number of employees.b.Interval scale; there is no absolute zero point for temperature.c.Nominal scale; we could use "1" to identify yes and "0" for no.d.Ordinal scale; the cars are ranked but there is no measure for the distance between them.1.19d/p/m It will help them become more intelligent consumers of statistical claims and findings.Whether as citizens or as business professionals, such individuals will bebetter able toprotect themselvesfromthose in business or the media who maybe either incompetent or unethical.1.20d/p/ma.Major: nominal. Each major would be assigned a number.b.Class: ordinal–Freshman, Sophomore, Junior, or Senior.c.SAT score: interval. This value gives him a ranking and there is a unit of measurement, but multiplesdo not make sense. (The minimum total score is 400, not zero.)d.The $30 used to buy a new calculator: ratio.1.21d/p/ma.The population would be all 40 students who are enrolled in the English class. The sample would bethe 5 students in the class that Roger questioned.b.This is probably not a representative sample, since Roger chose 5 students that always sit in the back.They may all be friends or may have different opinions than those sitting in the front.1.22d/p/ma.This information can be viewed as representing the nominal scale of measurement if we view thestocks in terms of returning more versus not returning more than the rate that had been expected.b.This information can be viewed as representing the ratio scale of measurement. For example, a 40%rate for above-expected performance would be twice a 20% rate. There is an absolute zero, a unit ofmeasurement (percentage point), and multiples are meaningful.

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5CHAPTER 2VISUAL DESCRIPTION OF DATASECTION EXERCISES2.1d/p/e A frequency distribution is a table that divides the data values into classes and shows thenumber of observed values that fall into each class. By summarizing and reporting data into a frequencydistribution, the data can be readily understood and interpreted.2.2d/p/m Selecting the number of classes is a subjective process. In general, about 5 to 15 classes will besuitable.2.3c/p/ma.45.59 millionb. lower limit is 35, upper limit is under 45c. 10 yearsd.40 years2.4c/p/ma.40.78 millionb. lower limit is 25, upper limit is under 35c. 10 yearsd.30 years2.5c/p/ma.183.53 thousandb. lower limit is 45, upper limit is under 55c. 10 yearsd.50 years2.6c/p/ma.34.23 thousandb. lower limit is 15, upper limit is under 25c. 10 yearsd.20 years2.7d/p/e Mutually exclusive means a given data value can fall into only one class. Exhaustive means thatthe set of classes includes all possible data values.2.8c/p/m The number of states in each category is shown above the corresponding bar. For example,there are 13 states within the $50 billion–under$100 billion category.8007006005004003002001000181614121086420DepositsFrequency110000101113751316Histogram of Deposits2.9c/p/m The number of employees in each category is shown above the corresponding bar.

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6For example, there are 7 data values within the 20–under22 category.wageFrequency262422201816987654321028785Histogram of wage2.10c/p/m The number of applicants in each category is shown above the corresponding bar.For example, there were 9 applicants within the 70–under80 category.ScoreFrequency11010090807060509876543210155941Histogram of Score2.11c/p/m The number of seasons in each goal category is shown above the bars. For example, therewere 2 seasons during which Mr. Gretzky’s goal total was in the 70–under80 category.

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7GoalsFrequency100806040200432101121432321Histogram of Goals2.12c/a/mAnnual SalesPercentCumulative FrequencyUnder $10,00059.301262$ 10,000-under $ 25,00012.031518$ 25,000-under $ 50,0007.421676$ 50,000-under $ 100,0006.581816$ 100,000-under $ 250,0007.471975$ 250,000-under $500,0003.852057$500,000-under $1,000,0001.972099$1,000,000 or more1.3621282.13c/a/mDriver AgePercentCumulative FrequencyUnder 205.2910.7220-under 258.3127.5625-under 3520.1268.3435-under 4522.49113.9345-under 5518.10150.6355-under 6511.50173.9565 or older14.19202.712.14c/a/mTotal Deposits, $ BillionsRelative Frequency, %Greater-Than or Within, %0-under 10058.0100.0

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8100-under 20024.042.0200-under 3008.018.0300-under 4004.010.0400-under 5002.06.0500-under 6000.04.0600-under 7000.04.0700–under 8004.04.02.15c/a/m Less-than Ogive for 50 U.S. States:123456789101112131415161718ABCDEFGHIDeposits Percent0050321005815068200822508830090350924009445094500965509660096650967009675098800100Less-Than Ogive for 50 U.S. States0204060801001200200400600800Deposits, $BillionsPercent2.16c/p/m12345678910111213141516ABCDEFGHIGoalsPercent0010520153030404050556075708080909095100100Less-Than Ogive for Gretzky Goals Scored020406080100020406080100Goals Scored% of Seasons2.17c/c/mThe number of data values in each category is shown above the bar.For example, there are 10 data valuesin the $30,000–under$40,000 category. There are two portfolio values at the extremes that seemespecially low or high compared to the others.

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9PortfolioFrequency8000060000400002000020151050171820191041Histogram of Portfolio2.18c/c/m The number of data values in each category is shown above the bar. For example, there wasonly one data value in the28seconds–under30seconds category, and this seems to be an especially lowtime compared to the others.48444036322820151050SecondsFrequency027921201370010Histogram of Seconds2.19c/c/m The number of data values in each category is shown above the bar. For example, there are23data values in the55–under 60e-mails category. The single valuesin the40–under 45and 45–under50 categories would appear to be especially low compared to the others.

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1080706050402520151050emailsFrequency6814182023911Histogram of emails2.20c/p/m2.21c/p/mStem (Tens)|Leaf (Units)Stem (Tens)|Leaf (Units)1|5591|137992|0145672|244468893|4583|00233794|126884|11233666895|175|223346777996|244796|01137|12578|132.22c/p/m2020222227283031313335394143444454572.23c/p/d It is not possible to determine the exact values because there is not enough detail to determinethe units digit. One possible set of data is shown below:6136957708999556307028649009626337088669039816527218849096777558979362.24c/c/mStem-and-Leaf Display: PortfolioStem-and-leaf of PortfoliN= 80Leaf Unit = 1000

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1111 942 03352 7103 12234153 66788254 0111222233344 566668899(9)5 001133334375 55566777899266 001111222176 67777888987 00333427 618 0Portfolio8000072000640005600048000400003200024000Dotplot of Portfolio2.25c/c/mStem-and-Leaf Display: SecondsStem-and-leaf of SecondsN= 80Leaf Unit = 0.10

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1212911301311321333347983545557123605892137145677999293804556689(12)39122344457778394001123334567892641003577781842033359124313594422249445662465645.042.540.037.535.032.530.0SecondsDotplot of Seconds2.26c/c/mStem-and-Leaf Display: emailsStem-and-leaf of emailsN= 100

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13Leaf Unit = 1.014124911500222234434555555566778888888999999(20)6001111122233344444444665555666677777778992870000111122224414755666777680001348478726660544842emailsDotplot of emails2.27c/c/mStem-and-Leaf Display: AppraisalStem-and-leaf of AppraisaN= 60Leaf Unit = 1012 152 2233122 4445555202 66666777252 99999(8)3 00000001273 22233333193 444455555103 67773 88899914 1

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14Appraisal420390360330300270240210Dotplot of Appraisal2.28c/c/mStem-and-Leaf Display: metersStem-and-leaf of metersN= 80Leaf Unit = 1.027 1277 56789198 001111233444378 555556666777889999(19)9 0011111222333333344249 55666666789991110 00112344310 78111 2meters1081029690847872Dotplot of meters

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152.29d/p/m A histogram graphically displays class intervals as well as class frequencies. A bar chartdisplays the frequencies for a set of categories or classes. Histograms are appropriate for quantitative data,while bar charts are better for qualitative data.2.30c/a/mBar Chart of market shares in 2007:1234567891011121314151617ABCDEFGHI2007N. America69.0Japan15.5Germany7.4Other8.12007 Market Shares01020304050607080N. AmericaJapanGermanyOtherRegion of ManufactureMarket Share2.31c/p/m

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1612345678910111213141516ABCDEFGHIYearIncome19934516119944701219954968719965151819975335019985606119995998120006222820016327820026273220036509340000450005000055000600006500070000199319951997199920012003YearMedian family income, $Income2.32c/p/m12345678910111213141516ABCDEFGHYear$/share19981.1019991.3920001.4620011.2520020.7020031.1520041.7920052.0420062.8320071.9820083.76McDonald's Net Income Per Share0.001.002.003.004.005.0019961998200020022004200620082010Year$/Share2.33c/p/m12345678910111213141516ABCDEFGHIJYearincome/share dividends/share19981.100.1819991.390.2020001.460.2220011.250.2320020.700.2420031.150.4020041.790.5520052.040.6720062.831.0020071.981.5020083.761.63McDonald's Net Income/Share and Dividends/Share0.001.002.003.004.005.0019961998200020022004200620082010Year$/Shareincome/sharedividends/share2.34c/p/m

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