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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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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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$%ample

!xercise" Does the data always conclusi#ely

pro#e or dispro#e the theory$


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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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!escripti"e statistics

#nferential statistics

Tools of Business Statistics


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Statistical (nference

Statistical #nference%o use sampledata to make 'eneralizations

about a lar'er data set (population)


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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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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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$%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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*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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!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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*!( 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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uestion

Suppose you concluded ?A& Could you bewron' in your decision$ 2hat if you did notre@ect ?*$ Could you be wron' in your

decision$


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$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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!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: 5e@ectin' the null hypothesis is usuallyconsidered the more serious error thanacceptin' it&


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Type ( and (( $rrors

$ %ype I error %he chance of re@ectin' 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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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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Freuency )lot

2hich ba' would you choose$


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#ame ules

%he ob@ecti#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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$%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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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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!ecision ule 1

5e@ect the null hypothesisin fa#or of thealternati#e hypothesis ifthe #oucher #alue is

*&%ype I error $ '

%ype II error&


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Summary

!ecision *ule 5e@ect H*if #oucher **eection *egion * or more

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

are more extreme


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*!(5 !ecision ule 2

5e@ect the null hypothesisin fa#or of thealternati#e hypothesis ifthe #oucher #alue is

$%ype I error $ '

%ype II error&


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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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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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*!( 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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#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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$%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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*!( 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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Sampling Techniues

on"enience

Samples

&on-$robabilitySamples

udgement

$robability Samples

Simple

*andomSystematic

Stratifiedluster


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Statistical Sampling

Items of the sample are chosen based onknown or calculable probabilities

$robability Samples

Simple

*andom

SystematicStratified luster


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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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Simple andom Samples

!#ery indi#idual or item from the population

has an e,ual chanceof bein' selected


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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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$%ample


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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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"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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*!( 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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!ata Types

!ata

0ualitati"e

ategorical

0uantitati"e

&umerical

!iscrete ontinuous


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!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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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