McGraw-Hill/IrwinCopyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 1 An Introduction to Business Statistics

1-2 An Introduction to Business Statistics 1.1Populations and Samples 1.2Selecting a Random Sample 1.3Ratio, Interval, Ordinal, and Nominative Scales of Measurement (Optional) 1.4An Introduction to Survey Sampling (Optional) 1.5More About Data Acquisition and Survey Sampling (Optional)

1-3 Populations and Samples PopulationA set of existing units (usually people, objects or events) VariableA measurable characteristic of the population CensusAn examination of the entire population of measurements SampleA selected subset of the units of a population

1-4 Sample from Population Population Sample

1-5 Terminology Measurement Value Quantitative Qualitative Population of Measurement Census Sample Descriptive Statistics Statistical Inference

1-6 Measurement The process of determining the extent, quantity, amount, etc, of the variable of interest for some a particular item of the population. Produces data For example, collecting annual starting salaries of graduates from last year’s MBA program

1-7 Value The result of measurement. The specific measurement for a particular unit in the population For example, the starting salaries of graduates from last year’s MBA Program

1-8 Quantitative Measurements that represent quantities. (For example, “how much” or “how many.”) Annual starting salary is quantitative Age and number of children are also quantitative

1-9 Qualitative A descriptive category to which a population unit belongs: a descriptive attribute of a population unit. A person’s gender is qualitative A person’s hair color is also qualitative

1-10 Population of Measurements Measurement of the variable of interest for each and every population unit. Sometimes referred to as an observation For example, annual starting salaries of all graduates from last year’s MBA program

1-11 Census The process of collecting the population of all measurements is a census. Census usually too expensive, too time consuming, and too much effort for a large population

1-12 Sample A subset of population units. For example, a university graduated 8,742 students This is too large for a census So, we select a sample of these graduates and learn their annual starting salaries

1-13 Sample of Measurements Measured values of the variable of interest for the sample units For example, the actual annual starting salaries of the sampled graduates

1-14 Descriptive Statistics The science of describing the important aspects of a set of measurements. For example, for a set of annual starting salaries, want to know: –How much to expect –What is a high versus low salary If the population is small, could take a census and make statistical inferences But if the population is too large, then …

1-15 Statistical Inference The science of using a sample of measurements to make generalizations about the important aspects of a population of measurements. For example, use a sample of starting salaries to estimate the important aspects of the population of starting salaries

1-16 Selecting a Random Sample A random sample is a sample selected from a population so that: Each population unit has the same chance of being selected as every other unit –Each possible sample (of the same size) has the same chance of being selected

1-17 Random Sample Example Randomly pick two different people from a group of 15: –Number the people from 1 to 15 and write their numbers on 15 different slips of paper –Thoroughly mix the papers and randomly pick two of them –The numbers on the slips identifies the people for the sample

1-18 How to Pick? Sample with replacement Sample without replacement

1-19 Sample with Replacement Replace each sampled unit before picking next unit The unit is placed back into the population for possible reselection However, the same unit in the sample does not contribute new information

1-20 Sample Without Replacement A sampled unit is withheld from possibly being selected again in the same sample Guarantees a sample of different units –Each sampled unit contributes different information –Sampling without replacement is the usual and customary sampling method

1-21 Drawing the Random Sample If the population is large, use a table of random numbers In large sampling projects, tables of random numbers are often used to automate the sample selection process See Table 1.1 in the textbook for a table of random numbers –Portion on next slide

1-22 Portion of Random Number Table

1-23 Using Random Number Tables For a demonstration of the use of random numbers, read Example 1.1, “Cell Phone Case: Estimating Cell Phone Costs,” in the textbook Use random numbers to randomly select 100 employees from a bank with 2,136 employees Random numbers can be computer-generated

1-24 Approximately Random Samples In general, must make a list identifying each and every individual population unit –Called a frame If the population is very large, it may not be possible to list every individual population unit So instead draw a “systematic” sample

1-25 Systematic Sample Randomly enter the population and systematically sample every k th unit This usually approximates a random sample –Read Example 1.2, “Marketing Research Case: Rating a New Bottle Design,” in the textbook

1-26 Example 1.2: Rating a New Bottle Design Wish to determine consumer reaction to a new bottle design Will use the “mall intercept method” –Shoppers in a mall are intercepted and asked to participate in a consumer survey Asked to rate a new bottle

1-27 Example 1.2: Using Systematic Sample Cannot list and number every shopper –As a result, cannot use random numbers Instead, will use a systematic sample Every 100 th shopper is selected –Using every 100 th shopper is arbitrary Using widely spaced shoppers, can be reasonably sure not related

1-28 Problems With Non-Random Samples For presidential election of 1936, Literary Digest predicted Alf Landon would defeat Franklin D. Roosevelt Instead Roosevelt won in a landslide Literary Digest’s mistake was to sample names from telephone books and club membership rosters Many people did not have phones or belong to clubs –As a result, they were not included in sample –They voted overwhelmingly for Roosevelt

1-29 Voluntary Response Sample Participants select themselves to be in the sample –Participants “self-select” –For example, voting on American Idol –Commonly referred to as a “non-scientific” sample Usually not representative of the population –Over-represent individuals with strong opinions –Usually, but not always, negative opinions

1-30 Process A sequence of operations that takes inputs (labor, raw materials, methods, machines, etc) and turns them into outputs (products, services, and the like). Process Inputs Outputs Sampling a Process

1-31 Process “Population” The “population” from a process is all output produced in the past, present, and the future. For example, all automobiles of a particular make and model. For instance, the Chrysler Sebring Cars will continue to be made over time

1-32 Population Size Finite Infinite

1-33 Finite Population Finite if it is of fixed and limited size Finite if it can be counted –Even if very large –For example, all the Chrysler Sebring cars actually made during just this model year is a finite population Because a specific number of cars was made between the start and end of the model year

1-34 Infinite Population Infinite if it is unlimited Infinite if listing or counting every element is impossible –For example, all the Chrysler Sebring cars that could have possibly been made this model year is an infinite population

1-35 Statistical Control A process is in statistical control if it does not exhibit any unusual process variations. A process in statistical control displays a constant amount of variation around a constant level A process not in statistical control is “out of control”

1-36 Statistical Control Continued To determine if a process is in control or not, sample the process often enough to detect unusual variations. Issue: How often to sample? See Example 1.3, “The Car Mileage Case: Estimating Mileage,” in the textbook

1-37 Runs Plot A runs plot (or time series plot) is a graph of actual individual measurements of process output over time –Process output (the variable of interest) is plotted on the vertical axis against time plotted on the horizontal axis The constant process level is plotted as a horizontal line The variation is plotted as an up and down movement as time goes by of the individual measurements, relative to the constant level

1-38 Runs Plot

1-39 Temperature of Coffee Consider the coffee temperature case of Problem 1.12 Coffee was sampled every half hour from 10:00 AM to 9:30 PM, and its temperature measured –The 24 timed measurements are graphed in the runs plot

1-40 Temperatures Recorded

1-41 Runs Plot

1-42 Results Over time, temperatures appear to have a fairly constant amount of variation around a fairly constant level –The temperature is expected to be at the constant level shown by the horizontal blue line Sometimes the temperature is higher and sometimes lower than the constant level –About the same amount of spread of the values (data points) around the constant level The points are as far above the line as below it The data points appear to form a horizontal band So, the process is in statistical control –Coffee-making process is operating “consistently”

1-43 Outcome Because the coffee temperature has been and is presently in control, it will likely stay in control in the future –If the coffee making process stays in control, then coffee temperature is predicted to be between 152 o and 170 o F In general, if the process appears from the runs plot to be in control, then it will probably remain in control in the future –The sample of measurements was approximately random –Future process performance is predictable

1-44 Out of Control If there is a trend in the process performance –Future performance of the process will be outside established limits

1-45 Out of Control If, there is a constant level, but the amount of the variation is varying as time goes by –Data points fan out from or neck down to the constant level

1-46 Statistical Process Control The real purpose is to see if the process is out of control so corrective action can be taken if necessary Must investigate further to find out why the process is out of control