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

2. 1-2 Statistics When it is singular, it refers to the sciences of statistics that help us collect, organize, and interpret Data. When it is plural, it refers to the data themselves, especially those that describe or summarize something.

3. 1-3 Populations and Samples PopulationThe set of all elements about which we wish to draw conclusions (usually people, objects or events) VariableAny characteristic of an element is called a variable. MeasurementThe process of assigning a value of variable to each population unit. Usually it refers to the value itself.

4. 1-4 Measurement The process of determining the extent, quantity, amount, etc, of the variable of interest for a particular item of the population. Produces data For example, collecting annual starting salaries of graduates from last year’s MBA program

5. 1-5 Quantitative vs. Qualitative( Categorical ) Quantitative If the measurements are numbers representing how many or how much. Qualitative If the measurements are attributes, labels, or nonnumeric entries.

6. 1-6 Quantitative The possible measurements are numbers that represent quantities, ‘how many ’ or ‘how much’ A person’s weight is quantitative. A laptop’s price is also quantitative.

7. 1-7 When initiating a study, we first define our variable of interest, or response variable. Other variables, called factors, may be related to the response variable interest will also be measured. When analysts are unable to control the factors of interest, the study is called observational. If we are able to set or manipulate the values of these factors, we have an experimental study.

8. 1-8 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

9. 1-9 CensusAn examination of the entire population measurements SampleA selected subset of the units of a population

10. 1-10 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

11. 1-11 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

12. 1-12 Parameter vs. Statistic A parameter is a numerical description of a population characteristic. Example: the percentage of college students who use Dell computer. A statistic is a numerical description of a sample characteristic. Example: the percentage of students selected nationwide using Dell computer.

13. 1-13 Sample from Population Population Sample Parameter Statistic make inference

14. 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 …

15. 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

16. 1-16 Selecting a Random Sample A random sample is a sample selected from a population so that: Every element in the population has the same chance of being included in the sample. –Each possible sample (of the same size) has the same chance of being selected

17. 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

18. 1-18 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 next slide a table of random numbers

19. 1-19 Portion of Random Number Table

20. 1-20 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

21. 1-21 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

22. 1-22 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

23. 1-23 Systematic Sampling Select some starting point and then select every k th element in the population

24. 1-24 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

25. 1-25 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 reasonable sure not related

26. 1-26 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

27. 1-27 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

28. 1-28 Terminology Measurement Quantitative Qualitative Population of Measurement Census Sample Random Sample Descriptive Statistics Statistical Inference

29. 1-29 http://www.learner.org/vod/vod_window. html?pid=139 http://www.learner.org/vod/vod_window. html?pid=139 http://www.learner.org/vod/vod_window. html?pid=152 http://www.learner.org/vod/vod_window. html?pid=152