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    Fundamentals of Business Statistics - Spring 2006 1

    Business Statistics:A Decision-Making Approach

    6thEdition

    Chapter 1The Where, Why, and

    Ho of!ata "ollection

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    Fundamentals of Business Statistics - 2

    "hapter #oals

    After completing this chapter, you should

    be able to:

    Describe key data collection methods Learn to think critically about information

    Learn to examine assumptions

    Know key definitions

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    Fundamentals of Business Statistics - 3

    What is Statistics

    Statistics is the scienceof dataThe Scientific Method

    1. Formulate a theory

    2. Collect data to test the theory3.Analyze the results

    4. Interpret the results and make decisions

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    Fundamentals of Business Statistics - 4

    $%ample

    !xercise" Does the data always conclusi#ely

    pro#e or dispro#e the theory$

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    Fundamentals of Business Statistics - 5

    The Scienti&c 'ethod

    %he scientific method is an iterati#e process& In'eneral we reect a theory if the data wereunlikely to occur if the theory were in facttrue&

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    Fundamentals of Business Statistics - 6

    !escripti"e statistics

    #nferential statistics

    Tools of Business Statistics

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    Fundamentals of Business Statistics - 7

    Statistical (nference

    Statistical #nference%o use sampledata to make 'eneralizations

    about a lar'er data set (population)

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    Fundamentals of Business Statistics - 8

    A $opulationis the set of all items orindi#iduals of interest

    A Sampleis a subset of the population understudy so that inferences can be drawn from it

    Statistical inferenceis the process of drawin'

    conclusions about the population based oninformation from a sample

    )opulations and Samples

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    Fundamentals of Business Statistics - 9

    Testing Theories

    %ypotheses Competin' theories that we want to testabout a population are called Hypotheses instatistics& Specifically we label these competin'theories as Null Hypothesis (H*) andAlternativeHypothesis (H+or HA)&

    H*: %he null hypothesis is the status ,uo or thepre#ailin' #iewpoint&

    HA: %he alternati#e hypothesis is the competin' belief&It is the statement that the researcher is hopin' topro#e&

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    Fundamentals of Business Statistics - 10

    $%ample

    %akin' an aspirin e#ery other day for -* yearscan cut your risk of colon cancer nearly inhalf a study su''ests& Accordin' to theAmerican Cancer Society the lifetime risk of

    de#elopin' colon cancer is + in +.& H*"

    HA:

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    Fundamentals of Business Statistics - 11

    *ou !o (t 1+2

    (New York Times +/-+/+001) 2inter can 'i#e you a cold because it forcesyou indoors with cou'hers sneezers and wheezers& %oddlers can 'i#eyou a cold because they are the ori'inal 3erms 456 7s& 8ut can 'oin'postal with the boss or frettin' about marria'e 'i#e a person a post9nasal drip$

    :es say a 'rowin' number of researchers& A psycholo'y professor atCarne'ie ;ellon 7ni#ersity Dr& Sheldon Cohen said his most recentstudies su''est that stress doubles a person& %he researcher would like to assess if stress increases thispercenta'e& So the population of interest is people who are understress& State the appropriate hypothesis for assessin' the researcher

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    Fundamentals of Business Statistics - 12

    !eciding Which Theory toSupportDecision makin' is based on the 4rare e#ent6 concept&Since the null hypothesis is the status ,uo we

    assume that it is true unless the obser#ed result isextremely unlikely (rare) under the null hypothesis&

    !efinition" If the data were indeed unlikely to beobserved under the assumption that H*is true, and

    therefore we reect H*in favor of HA, then we say

    that the data are statistically significant!

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    Fundamentals of Business Statistics - 13

    *!( 1+

    Last month a lar'e supermarket chain recei#ed manycustomer complaints about the ,uantity of chips in a+.9ounce ba' of a particular brand of potato chips&2antin' to assure its customers that they were

    'ettin' their money

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    Fundamentals of Business Statistics - 14

    uestion

    Suppose you concluded ?A& Could you bewron' in your decision$ 2hat if you did [email protected] ?*$ Could you be wron' in your

    decision$

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    Fundamentals of Business Statistics - 15

    $rrors in !ecision 'a.ing

    In our current @ustice system the defendant ispresumed innocent until pro#en 'uilty& %henull and alternati#e hypothesis thatrepresents this is"

    H*"

    HA" %ruth

    H* HA

    :our decisionbased on data

    H*

    HA

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    Fundamentals of Business Statistics - 16

    !e&nition

    "eectin# the null hypothesis H* when in fact itis true is called a Type # error&Acceptin# thenull hypothesis H* when in fact it is not trueis called a Type ## error&

    &ote: [email protected]' the null hypothesis is usuallyconsidered the more serious error thanacceptin' it&

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    Fundamentals of Business Statistics - 17

    Type ( and (( $rrors

    $ %ype I error %he chance of [email protected]' H*when in fact

    H*is true

    %(HABH*)& %ype II error

    %he chance of acceptin' H*when in fact

    HAis true %(H*BHA)

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    Fundamentals of Business Statistics - 18

    What/s in the Bag

    'becti"e %o explore the#arious aspects of decisionmakin'

    $roblem statement %here aretwo identical lookin' ba's8a' A and 8a' 8& !ach ba'contains -* #ouchers& %hecontents of the ba' i&e& theface #alue and thefre,uency of #oucher#alues are as follows"

    Facealue () 8a' A 8a' 8

    9+*** + *

    +* 1 +

    -* . +E* - -

    =* - -

    * + .

    .* + 1

    +*** * +

    %otal -* -*

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    Fundamentals of Business Statistics - 19

    Freuency )lot

    2hich ba' would you choose$

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    Fundamentals of Business Statistics - 20

    #ame ules

    %he [email protected]#e is to pick 8a' 8& :ou will be shown only one of the ba's& :ou will be allowed to 'ather some data from the

    ba' and based on that information you mustdecide whether to take the shown ba' (because you

    think that it is 8a' 8) or the other ba' (because youthink that the shown ba' is 8a' A)&

    Initially the data will consist of selectin' @ust one#oucher from the shown ba' (without lookin' into it)&In this case we say that we are takin' a sample ofsize n +&

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    Fundamentals of Business Statistics - 21

    $%ample 3cont+4

    ?*" %he shown ba' is 8a' A?A" %he shown ba' is 8a' 8

    %ype I error G %ype II error H

    ()ercise:If the #oucher you selected was .*

    what would you decide$ 2hat if the #oucherwas +* instead

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    Fundamentals of Business Statistics - 22

    Forming a !ecision ule

    2hat #alues of the#oucher (or in whatdirection of #oucher#alues) support the

    alternati#e hypothesis?A$ %hat is what is the

    direction of extreme$

    Facealue ()

    Chanceif 8a' A

    Chanceif 8a' 8

    9+*** +/-* *

    +* 1/-* +/-*-* ./-* +/-*

    E* -/-* -/-*

    =* -/-* -/-*

    * +/-* ./-*.* +/-* 1/-*

    +*** * +/-*

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    Fundamentals of Business Statistics - 23

    !ecision ule 1

    [email protected] the null hypothesisin fa#or of thealternati#e hypothesis ifthe #oucher #alue is

    *&%ype I error $ '

    %ype II error&

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    Fundamentals of Business Statistics - 24

    Summary

    !ecision *ule [email protected] H*if #oucher **eection *egion * or more

    +e say ... the cutoff is * and lar'er #alues

    are more extreme

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    Fundamentals of Business Statistics - 25

    *!(5 !ecision ule 2

    [email protected] the null hypothesisin fa#or of thealternati#e hypothesis ifthe #oucher #alue is

    $%ype I error $ '

    %ype II error&

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    Fundamentals of Business Statistics - 26

    Why Sample

    A (ensusis a sample of the entire population

    FIJIS?!D FIL!S A5! %?! 5!S7L% F :!A5S F SCI!J%IFIC

    S%7D: C;8IJ!D 2I%? %?! !M!5I!JC! F ;AJ: :!A5S

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    Fundamentals of Business Statistics - 27

    The anguage of Sampling Apopulationor uni#erse is the total elements of interest for a

    'i#en problem& Finite population Infinite population

    A sampleis a part of the population under study selected so thatinferences can be drawn from it about the population& Sample

    sizes are usually represented by n& Samplin# error )variation*is the difference between the result

    obtained from a sample and the result that would be obtainedfrom a census&

    %arametersare numerical descripti#e measures of populations /

    processes& Statisticsare numerical descripti#e measures computed from the

    obser#ations in a sample&

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    Fundamentals of Business Statistics - 28

    *!( 2+1

    ()ercise Nine percent of the +S population

    has Type blood! In a sample of -..

    individuals from the +S population, /0!12

    were found to have Type blood! (ircle your

    answer: In this particular situation the #alue 0> is a

    (parameter statistic)

    In this particular situation the #alue +-&> isa (parameter statistic)

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    Fundamentals of Business Statistics - 29

    #ood !ata

    A samplin' method is biasedif it produces results that

    systematically differ from the truth about the population&()ampleCon#enience samples and #olunteer samples 'enerally

    lead to biased samples&

    Selection biasis the systematic tendency on the part of thesamplin' procedure to exclude or include a certain part of thepopulation

    Nonresponse biasis the distortion that can arise because a lar'enumber of units selected for the sample do not respond&

    "esponse biasis the distortion that arises because of the wordin'of a ,uestion or the beha#ior of the inter#iewer&

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    Fundamentals of Business Statistics - 30

    $%ample

    In the election of +0E. the Literary Di'est ma'azinepredicted that challen'er Alf Landon would beat theincumbent Franklin 5oose#elt& %hey based theirprediction on a sur#ey of ten million citizens takenfrom lists of car and telephone owners of whom

    o#er -&E million responded& %his was the lar'estresponse to any poll in history and based on thisthe Literary Di'est predicted that Landon would win1> to =E>& In reality 5oose#elt won .-> to EN>&

    2hat went wron'$ At the same time a youn' manknown as 3eor'e 3allup sur#eyed **** peopleand correctly predicted that 5oose#elt would win theelection&

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    Fundamentals of Business Statistics - 31

    *!( 2+

    A study was conducted to estimate the a#era'e size ofhouseholds in the 7S& A total of +*** people wererandomly selected from the population and theywere asked to report the number of people in theirhousehold& %he a#era'e of these +*** responseswas found to be =&.&

    1. 2hat is the population of interest$

    2. 2hat is the parameter of interest$

    3.An a#era'e computed in this manner tends to belar'er than the true a#era'e size of households inthe 7S& %rue or false$ !xplain&

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    Fundamentals of Business Statistics - 32

    Sampling Techniues

    on"enience

    Samples

    &on-$robabilitySamples

    udgement

    $robability Samples

    Simple

    *andomSystematic

    Stratifiedluster

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    Fundamentals of Business Statistics - 33

    Statistical Sampling

    Items of the sample are chosen based onknown or calculable probabilities

    $robability Samples

    Simple

    *andom

    SystematicStratified luster

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    Fundamentals of Business Statistics - 34

    Statistical SamplingA samplin# method that #ives each unit in the

    population a known, non34ero chance ofbein# selected is called aprobability

    sampling method)statistical samplin#*!

    $robability Samples

    Simple

    *andom

    SystematicStratified luster

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    Fundamentals of Business Statistics - 35

    Simple andom Samples

    !#ery indi#idual or item from the population

    has an e,ual chanceof bein' selected

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    Fundamentals of Business Statistics - 36

    Strati&ed SamplesA stratified random sample is selected by

    dividin# the population into mutuallyexclusive sub#roups, and then takin# asimple random sample from each sub#roup!The simple random samples are thencombined to #ive the full sample!

    allows us to obtain information about eachSub'roup

    can be more efficient than simple randomsamplin'

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    Fundamentals of Business Statistics - 37

    $%ample

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    Fundamentals of Business Statistics - 38

    For a 1-in-/ systematic sample you orderthe units of the population in some way andrandomly select one of the first k units in theordered list& %his selected unit is the first unitto be included in the sample& :ou continuethrou'h the list selectin' e#ery kth unit fromthen on&

    Con#enient Fast Could be biased

    Systematic Samples

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    Fundamentals of Business Statistics - 39

    "luster SamplesIn cluster sampling the units of the population are 'rouped into

    clusters& ne or more clusters are then selected at random& If acluster is selected that all units of that cluster are part of thesample&

    Thin/ about it

    Is a cluster sample a simple random sample$ Is a cluster sample a stratified random sample$ 2ere you to form clusters how should the #ariability of the units

    within each cluster compare to the #ariability between theclusters$

    Is this criterion the same as in stratified random samplin'$

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    Fundamentals of Business Statistics - 40

    *!( 2+1

    Identify the samplin' method for each of the followin' scenarios"

    +& A shipment of +*** E oz& bottles of colo'ne has arri#ed to amerchant& %hese bottles were shipped to'ether in * boxes with-* bottles in each box& f the * boxes boxes were randomlyselected& %he a#era'e content for these +** bottles wasobtained&

    -& A faculty member wishes to take a sample from the +.**students in the school& !ach student has an ID number& A list ofID numbers is a#ailable& %he faculty member selects an IDnumber at random from the first +. ID numbers in the list andthen e#ery sixteenth number on the list from then on&

    E& A faculty member wishes to take a sample from the +.**students in the school& %he faculty member decides to inter#iewthe first +** students enterin' her class next ;onday mornin'&

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    Fundamentals of Business Statistics - 41

    !ata Types

    !ata

    0ualitati"e

    ategorical

    0uantitati"e

    &umerical

    !iscrete ontinuous

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    Fundamentals of Business Statistics - 42

    !ata Types

    Time Series !ata rdered data #alues obser#ed o#er time

    ross Section !ata Data #alues obser#ed at a fixed point in time

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    Fundamentals of Business Statistics - 43

    7ey !e&nitions

    A populationis the entire collection ofthin's under consideration A parameteris a summary measure computed

    to describe a characteristic of the population

    A sampleis a portion of the population

    selected for analysis

    A statisticis a summary measure computed todescribe a characteristic of the sample

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    ;akin' statements about a population byexaminin' sample results

    Sample statistics Mopulation parameters

    (known)#nference

    (unknown but can

    be estimated from

    sample e#idence)

    Sample Mopulation

    (nferential Statistics

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