Chapter 1:Introduction to Statistics Chapter 1Introduction to StatisticsLEARNING OBJECTIVESThe primary objective of Chapter 1 is to introduce you to the world ofstatistics, thereby enabling you to:1!ist "uantitative and graphical e#amples of statistics within a businessconte#t$%efine important statistical terms, including population, sample, andparameter, as they relate to descriptive and inferential statistics&'#plain the difference between variables, measurement, and data (Compare the four different levels of data: nominal, ordinal, interval, and ratioCHAPTER TEACHING STRATEGIn chapter 1 it is very important to motivate business students to study statistics bypresenting them with many applications of statistics in businessThe definition of statistics as a science dealing with the collection, analysis, interpretation, and presentationof numerical data is a very good place to startStatistics is about dealing with data%ataare found in all areas of businessThis is a time to have the students brainstorm on the wide variety of places in business where data are measured and gatheredIt is important to define statistics for students because they bring so many preconceptions of the meaning of the term)or this reason, several perceptions of the word statistics is given inthe chapterChapter 1 sets up the paradigm of inferential statisticsThe student will understand that while there are many useful applications of descriptive statistics in business, the strength of the application of statistics in the field of business is through inferential statistics)rom this notion, we will later introduce probability, sampling, confidence intervals, and hypothesis testingThe process involves ta*ing a sample from the population, computing a statistic on the sample data, and ma*ing an inference +decision or conclusion, bac* to the population from which the sample has been drawnIn chapter 1, levels of data measurement are emphasi-edToo many te#ts present data to the students with no comment or discussion of how the data were gathered or the level of data measurementIn chapter ., there is a discussion of sampling techni"ues/owever, in this chapter, four levels of data are discussedIt is important for students to understand that the statistician is often given data to analy-e without input as to how it was gathered or the type of measurementIt is incumbent upon statisticians and researchers to ascertain the level of measurement that the data represent so that appropriate techni"ues can be used in analysis0ll techni"ues presented in this te#t cannot be appropriately used to analy-e all dataChapter 1:Introduction to Statistics CHAPTER O!TLINE11 Statistics in 1usiness1$ 1asic Statistical Concepts1& 2ariables and %ata1( %ata 3easurement4ominal !evel5rdinal !evelInterval !evel6atio !evelComparison of the )our !evels of %ataStatistical 0nalysis 7sing the Computer: '#cel and 3initab"E TER#SCensus 5rdinal !evel %ata%ata8arameter%escriptive Statistics 8arametric StatisticsInferential Statistics 8opulationInterval !evel %ata 6atio !evel %ata3easurementSample3etric %ata Statistic4ominal !evel %ata Statistics4onmetric %ata 2ariable4onparametric StatisticsSOL!TIONS TO PROBLE#S IN CHAPTER 111 '#amples of data in functional areas:accounting 9 cost of goods, salary e#pense, depreciation, utility costs, ta#es, e"uipment inventory, etcfinance 9 :orld ban* bond rates, number of failed savings and loans, measured ris* ofcommon stoc*s, stoc* dividends, foreign e#change rate, li"uidity rates for a single9family, etcChapter 1:Introduction to Statistics human resources 9 salaries, si-e of engineering staff, years e#perience, age of employees, years of education, etcmar*eting 9 number of units sold, dollar sales volume, forecast sales, si-e of sales force, mar*et share, measurement of consumer motivation, measurement of consumer frustration, measurement of brand preference, attitude measurement, measurement of consumer ris*, etcinformation systems 9 C87 time, si-e of memory, number of wor* stations, storage capacity, percent of professionals who are connected to a computer networ*, dollar assets of company computing, number of ;hits< on the Internet, time spent on the Internet per day, percentage of people who use the Internet, retail dollars spent in e9commerce, etcproduction 9 number of production runs per day, weight of a product= assembly time, number of defects per run, temperature in the plant, amount of inventory, turnaround time, etcmanagement 9 measurement of union participation, measurement of employer support, measurement of tendency to control, number of subordinates reporting toa manager, measurement of leadership style, etc1$ '#amples of data in business industries:manufacturing 9 si-e of punched hole, number of rejects, amount of inventory, amount of production, number of production wor*ers, etcinsurance 9 number of claims per month, average amount of life insurance per family head, life e#pectancy, cost of repairs for major auto collision, average medical costs incurred for a single female over (> years of age, etctravel 9 cost of airfare, number of miles traveled for ground transported vacations, number of nights away from home, si-e of traveling party, amount spent per day on besides lodging, etcretailing 9 inventory turnover ratio, sales volume, si-e of sales force, number of competitors within $ miles of retail outlet, area of store, number of sales people, etccommunications 9 cost per minute, number of phones per office, miles of cable per customer head"uarters, minutes per day of long distance usage, number of operators, time between calls, etccomputing 9 age of company hardware, cost of software, number of C0%?C03 stations, age of computer operators, measure to evaluate competing software pac*ages, si-e of data base, etcChapter 1:Introduction to Statistics agriculture 9 number of farms per county, farm income, number of acres of corn per farm, wholesale price of a gallon of mil*, number of livestoc*, grain storage capacity, etcban*ing 9 si-e of deposit, number of failed ban*s, amount loaned to foreign ban*s,number of tellers per drive9in facility, average amount of withdrawal from automatic teller machine, federal reserve discount rate, etchealthcare 9 number of patients per physician per day, average cost of hospital stay, average daily census of hospital, time spent waiting to see a physician, patient satisfaction, number of blood tests done per wee*1& %escriptive statistics in recorded music industry 9 1, 6C0 total sales of compact discs this wee*, number of artists under contract to a company at a given time$, total dollars spent on advertising last month to promote an album&, number of units produced in a day(, number of retail outlets selling the company@s productsInferential statistics in recorded music industry 9 1, measure the amount spent per month on recorded music for a few consumers then use that figure to infer the amount for the population$, determination of mar*et share for rap music by randomly selecting a sample of >AA purchasers of recorded music&, %etermination of top ten single records by sampling the number of re"uests at a few radio stations(, 'stimation of the average length of a single recording by ta*ing a sample of records and measuring themThe difference between descriptive and inferential statistics lies mainly in the usage of the dataThese descriptive e#amples all gather data from every item in the population about which the description is being made)or e#ample, 6C0 measures the sales on all its compact discs for a wee* and reports the totalIn each of the inferential statistics e#amples, a sample of the population is ta*en and the population value is estimated or inferred from the sample)or e#ample, itmay be practically impossible to determine the proportion of buyers who prefer Chapter 1:Introduction to Statistics rap music/owever, a random sample of buyers can be contacted and interviewed for music preferenceThe results can be inferred to population mar*et share1( %escriptive statistics in manufacturing batteries to ma*e better decisions 91, total number of wor*er hours per plant per wee* 9 help management understand labor costs, wor* allocation, productivity, etc $, company sales volume of batteries in a year 9 help management decide if the product is profitable, how much to advertise in coming year, compare to costs to determine profitability&, total amount of sulfuric acid purchased per month for use in battery production 9 can be used by management to study wasted inventory, scrap, etcInferential Statistics in manufacturing batteries to ma*e decisions 91, ta*e a sample of batteries and test them to determine the average shelf life 9 use the sample average to reach conclusions about all batteries of this type3anagement can then ma*e labeling and advertising claimsThey can compare these figures to the shelf9 life of competing batteries$, Ta*e a sample of battery consumers and determine how many batteries they purchase per yearInfer to the entire population 9 management can use this information to estimate mar*et potential and penetration&, Interview a random sample of production wor*ers to determine attitude towards company management 9 management can use this survey results to ascertain employee morale and to direct efforts towards creating a more positive wor*ing environment which, hopefully, results in greater productivity1> 1, Si-e of sale +B, per customer in menCs formal wear'ither by ta*ing a sample or using a census, management could compute the average sale in menCs formal wear of a wee*ly period and compare the number to the same average ta*en a year ago or a month ago to determine if more is being sold per customer5ther variables might include number of sales per hour, number of people entering the department per day, number of dress shirts sold per day, etc$, 4umber of employees wor*ing per dayThis variable could indicate the day of the wee* +certain days have more or less sales,, sales activity +how sales are doing overall,, or even health of associates5ther variables might include percent of employees absent due to illness, average number of hours wor*ed per wee* per employee, number of open positions, etcChapter 1:Introduction to Statistics &,Inventory turnover rate/ow fast are items in the store sellingD5ther variables migh include reorder rate, percent of storage space utili-ed, number of stoc*outs per wee*, etc(, 4umber of customers that enter the store per hourThis figure will vary by day, time of day, and seasonCompare figures on this variable from period to period can give some indication of sales trends which can help drive human resource planning, etc5ther variables might include amountof time spent per customer in the store per visit, distance that customers travel to shop in the store, number of referrals that customers ma*e to other people annually, etc >, 8ercentage of people paying with cash8ercentage of people using credit cardsThese can be used to e#pedite pay systems, investigate employee theft, calculate surcharges associated with credit cards, etc5ther variables might include average time per chec*out, average wait time in pay line, etc 1E 1,Si-e of bill or tabThis variable is the total amount in dollars spent by a patron per visit to the restaurantThe bill or tab could be for an individualor a group and would include both food and beverages if they are all included in the bill5f course, the measurement would be in dollarsThisinformation could be very useful for the manager or owner to *now the average si-e of a bill both in projecting out total revenues over a period or as a baseline before a mar*eting effort to increase sales$, 8ercentage of Capacity )illedThis variable could be measured at various intervals, times, and days of the wee*The measurement would be calculated by ta*ing the number of patrons in the restaurant at any one time divided by the total number of seats in the restaurant +capacity,)rom this, management could ma*e staffing decisions for various times and days of the wee*In addition, management could ma*e decisions about when to e#pand, how much to advertise, and?or when to run specials&, !ength of StayThe measurement is how many minutes people are actually in the restaurant from the time they are assigned a table until they are leavingD)rom this, management could determine customer turnover rates which have capacity implicationsThat is, how many times in a day is an average table ;turned over9minute intervals The measurement is how manycustomers arrive at the front door to be greeted by the maFtre Gd in any given five9minute periodThis figure will li*ely vary by day of the wee*, Chapter 1:Introduction to Statistics season of the year, and time of day3anagement can use this information for staffing decisions and planning1. a, ratiob, ratioc, ordinald, nominale, ratiof, ratiog, nominalh, ratio1H a,ordinalb,ratioc,nominald,ratioe,intervalf,intervalg,nominalh,ordinal1I a, The population for this study is the IAA electric contractors who purchased6athburn wireb, The sample is the randomly chosen group of thirty9five contractorsc, The statistic is the average satisfaction score for the sample of thirty9five contractorsd, The parameter is the average satisfaction score for all IAA electric contractors in the population