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Business'Statistics MGT122 Part'I Ch.'17273 Dr.'Serena'Sandri 1

Organizational issues ! Office'hours ! Su.'11.00712.30 ! Tue.'11.00712.30

! Contact ! Office'location:'B305 ! [email protected]

Dr.'Serena'Sandri

2

Syllabus

Textbook'and'grading'policy ! Textbook ! Berenson,'Krehbiel and'Levine,' 2012,'Basic'Business' Statistics:'Concepts' and'Applications,' 12th'Edition

! Grading'policy ! ! ! !

First'exam'(25%) Second' exam'(25%) Final'exam,'comprehensive!' (40%) Quizzes'(10%)

! Attendance'is'compulsory ! Max'15%'(justified)'absences'will'be'tolerated Dr.'Serena'Sandri

4

Aim'and'Concept'of'the'Course ! The'course'deals'with'basic'statistical'concepts'and' methods'that'are'commonly'used'for'business'and' economic'applications ! The'course'introduces'the'students'to'statistical' methods'of'collection,'analysis,'and'presentation'of' quantitative'data ! Emphasis'will'be'on'the'use'of'both'descriptive'and' inferential'statistical'techniques'within'the'workplace ! Topics'covered'include'descriptive'statistics,' probability,'discrete'and'continuous'distributions,' confidence'intervals,'and'hypothesis'testing ! Acquired'knowledge'should'help'students'to'deal'with' applications'from'all'functional'areas'of'business. Dr.'Serena'Sandri

5

Content'of'the'Course ! Topics Chapter' 1:'Introduction Chapter' 2:'Organizing'and'Visualizing'Data Chapter' 3:'Numerical' Descriptive' Measures Chapter' 4:'Basic'Probability Chapter' 5:'Some'Important'Discrete'Probability' Distributions ! Chapter' 6:'The'Normal'Distribution' and'Other' Continuous' Distributions ! Chapter' 8:'Confidence' Interval'Estimation ! Chapter' 9:'Fundamental' of'Hypothesis'Testing ! ! ! ! !

Dr.'Serena'Sandri

6

Chapter'1

INTRODUCTION

7

Why'Learn'Statistics Make-better-sense-of-the-world

Make-better-business-decisions

• Internet'articles'/'reports • Magazine'articles

• Business'memos • Business'research

• Newspaper'articles • Television' &'radio'reports

• Technical'journals • Technical'reports

Chap'178 Chap'178

Uses'of'Statistics ! To'summarize'business'data ! To'draw'conclusions'from'business'data ! To'make'reliable'forecasts'about'business' activities ! To'improve'business'processes

Chap'179 Chap'179

Branches'Of'Statistics StatisticsThe'branch'of'mathematics'that'transforms'data'into' useful'information'for'decision'makers.'

Descriptive-Statistics Collecting,'summarizing,' presenting'and'analyzing' data

Inferential-Statistics Using'data'collected'from'a' small'group'to'draw' conclusions'about'a'larger' group

Chap'1710 Chap'1710

Descriptive'Statistics ! Collect'data ! e.g.,'Survey

! Present'data ! e.g.,'Tables'and'graphs

! Characterize'data ! e.g.,'The'sample'mean

Chap'1711 Chap'1711

Inferential'Statistics ! Estimation ! e.g.,'Estimate'the'population' mean'weight'using'the'sample' mean'weight

! Hypothesis'testing ! e.g.,'Test'the'claim'that'the' population'mean'weight'is'120' pounds Drawing-conclusions-about-a-large-group-of-individuals-based-on-a-smallergroup. Chap'1712 Chap'1712

Basic'Concepts ! VARIABLES ! Variables'are'characteristics'of'an'item'or'individual ! They'are'what'you'analyze'when'you'use'a'statistical' method.

! DATA ! Data'are'the'different'values'associated'with'a'variable.

! OPERATIONAL'DEFINITIONS ! Data'values'are'meaningless'unless'their'variables'have' operational'definitions,'universally'accepted'meanings' that'are'clear'to'all'associated'with'an'analysis.'

13

Basic'Concepts ! POPULATION ! A'population-consists'of'all'the'items'or'individuals' about'which' you'want'to'draw'a'conclusion.''The'population'is'the'“large' group.”

! SAMPLE ! A'sample-is'the'portion'of'a'population'selected' for'analysis.'' The'sample'is'the'“small'group.”

! PARAMETER ! A'parameter-is'a'numerical' measure'that'describes' a' characteristic'of'a'population.

! STATISTIC ! A'statistic-is'a'numerical'measure' that'describes'a'characteristic' of'a'sample. 14

Population'vs.'Sample Population

Measures' used'to'describe' the' population'are'called'parameters

Sample

Measures' used'to'describe' the' sample'are'called'statistics

Chap'1715 Chap'1715

Types'of'Variables ! Categorical (qualitative)'variables'have'values' that'can'only'be'placed'into'categories,'such' as'“yes”'and'“no.”' ! Numerical (quantitative)'variables'have' values'that'represent'quantities. ! Discrete variables'arise'from'a'counting-process ! Continuous variables'arise'from'a'measuringprocessChap'1716 Chap'1716

Types'of'Variables Variables

Categorical

Numerical-

Examples: " " "

Marital-Status Discrete Political-Party Eye-Color Examples: (Defined-categories) " Number-ofChildren " Defects-per-hour (Counted-items)

Continuous Examples: " "

Weight Voltage (Measuredcharacteristics)

17

Levels'of'Measurement ! There'are'four'essential'types'of'scales'with' which'variables'can'be'measured 1. 2. 3. 4.

Nominal'scale Ordinal'scale Interval'scale Ratio'scale

18

Levels'of'Measurement ! Nominal'scale ! classifies'data'into'distinct'categories'in'which'no'ranking' is'implied

! E.g. ! PC'ownership'(yes/no) ! Gender'(M/F) ! Nationality

19

Levels'of'Measurement ! Ordinal'scale ! classifies'data'into'distinct'categories'in'which' ranking'is'implied' Categorical-Variable------------

Ordered-Categories

Student( class(designation

Freshman,(Sophomore,( Junior,( Senior

Product(satisfaction

Satisfied,(Neutral,(Unsatisfied

Faculty(rank

Professor,(Associate(Professor,( Assistant(Professor,(Instructor

Standard(&(Poor’s(bond(ratings

AAA,(AA,(A,(BBB,(BB,(B,(CCC,(CC,( C,(DDD,(DD,(D

Student( Grades

A,(B,(C,(D,(F

Chap'1720 Chap'1720

Levels'of'Measurement ! Interval'scale ! ordered'scale'in'which'the'difference'between' measurements'is'a'meaningful'quantity'but'the' measurements'do'not'have'a'true'zero'point' (negative'values'can'be'used'and'the'zero'is' arbitrary)

! A'ratio'scale ! ordered'scale'in'which'the'difference'between'the' measurements'is'a'meaningful'quantity'and'the' measurements'have'a'true'zero'point.' Chap'1721 Chap'1721

Interval'and'Ratio'Scale ! ! ! ! ! ! !

Numerical variable Temperature (in'C'or F) Temperature (in'K) Height'(in'inches or cm) Weight (in'pounds or kg) Age'(in'years,'days) Salary (in'JD'or $)

Scale Interval Ratio Ratio Ratio Ratio Ratio 22

Properties'of'Scales

23

Properties'of'Scales

24

Chapter'2

ORGANIZING-AND-VISUALIZINGDATA 25

The'DCOVA'Process ! A'process'for'examining'and'concluding'from' data'is'helpful ! Define the'variables'for'which'you'want'to'reach' conclusions ! Collect the'data'from'appropriate'sources ! Organize the'data'collected'by'developing'tables ! Visualize the'data'by'developing'charts ! Analyze the'data'by'examining'the'appropriate' tables'and'charts'(and'in'later'chapters'by'using' other'statistical'methods)'to'reach'conclusions Chap'2726 Chap'2726

DCOVA ! Why'to'collect'data? ! A'marketing'research'analyst'needs'to'assess'the' effectiveness'of'a'new'television'advertisement. ! A'pharmaceutical'manufacturer'needs'to'determine' whether' a'new'drug'is'more'effective'than'those' currently' in'use. ! An'operations'manager'wants'to'monitor'a'manufacturing' process'to'find'out'whether'the'quality'of'the'product' being'manufactured'is'conforming'to'company'standards. ! An'auditor'wants'to'review'the'financial'transactions'of'a' company'in'order'to'determine'whether'the'company'is'in' compliance'with'generally'accepted'accounting'principles.

Chap'2727 Chap'2727

DCOVA'7 Sources'of'Data ! Primary'Sources:'The'data'collector'is'the'one'using' the'data'for'analysis ! Data'from'a'political'survey ! Data'collected'from'an'experiment ! Observed'data ! Secondary'Sources:'The'person'performing'data' analysis'is'not'the'data'collector ! Analyzing'census'data ! Examining'data'from'print'journals'or'data' published'on'the'internet.

Chap'2728 Chap'2728

DCOVA'7 Sources'of'data ! There'are'four'main'categories'of'sources'of' data 1. Data'distributed'by'an'organization'or'an' individual 2. A'designed'experiment 3. A'survey 4. An'observational'study

Chap'2729 Chap'2729

DCOVA'7 Sources'of'data 1. Data'distributed'by'an'organization'or'an' individual ! Stock'prices,'weather'conditions,'and'sports' statistics'in'daily'newspapers ! Financial'data'on'a'company'provided'by' investment'services ! Industry'or'market'data'from'market'research' firms'and'trade'associations

Chap'2730 Chap'2730

DCOVA'7 Sources'of'data 2. A'designed'experiment ! Consumer'testing'of'different'versions'of'a' product'to'help'determine'which'product'should' be'pursued'further ! Material'testing'to'determine'which'supplier’s' material'should'be'used'in'a'product ! Market'testing'on'alternative'product'promotions' to'determine'which'promotion'to'use'more' broadly Chap'2731 Chap'2731

DCOVA'7 Sources'of'data 3. A'survey ! Political'polls'of'registered'voters'during'political' campaigns ! People'being'surveyed'to'determine'their'satisfaction'with' a'recent'product'or'service'experience

4. An'observational'study ! Market'researchers'utilizing'focus'groups'to'elicit' unstructured'responses'to'open7ended'questions ! Measuring'the'time'it'takes'for'customers'to'be'served' in'a'fast'food'establishment ! Measuring'the'volume'of'traffic'through'an'intersection' to'determine'if'some'form'of'advertising'at'the' intersection'is'justified Chap'2732 Chap'2732

DCOVA'– Organizing'Data ! For'organizing'data,'it'should'be'considered' whether'data'are ! Categorical''(qualitative)'or ! Numerical'(quantitative)

! Categorical-data (categories)'can'be'organized' in'tables 1. One'categorical'variable'# summary'table 2. Two'categorical'variables'# contingency'table 33

DCOVA'– Categorical'Data ! Summary'table ! indicates'the'frequency,'amount,'or'percentage'of' items'in'a'set'of'categories'so'that'you'can'see' differences'between'categories ! Survey'data'on'1000'bank'customers Banking Preference? ATM Automated or live telephone

Percent 16% 2%

Drive-through service at branch

17%

In person at branch

41%

Internet

24% 34

DCOVA'– Categorical'Data ! Contingency'table ! Used'to'study'patterns'that'may'exist'between' the' responses'of'two'or'more'categorical' variables ! Cross'tabulates'(tallies)'jointly'the'responses'of'the' categorical' variables ! For'two'variables' the'tallies'for'one'variable' are' located'in'the'rows'and'the'tallies'for'the'second' variable'are'located'in'the'columns

! E.g.'a'supermarket'manager'wants'to'see'if' there'are'mistakes'on'invoices Chap'2735 Chap'2735

DCOVA'– Categorical'Data ! A'random'sample'of'400' invoices'is'drawn. ! Each'invoice'is'categorized' as'a'small,'medium,'or' large'amount. ! Each'invoice'is'also' examined'to'identify'if' there'are'any'errors. ! These'data'are'then' organized'in'the' contingency'table'to'the' right.

No Errors

Errors

Total

Small Amount

170

20

190

Medium Amount

100

40

140

Large Amount

65

5

335

65

70 400

Total

36

DCOVA'– Categorical'Data ! Contingency'tables'with'%'of'overall'total' No Errors

Errors

42.50%'='170'/'400 25.00%'='100'/'400 16.25%'='''65'/'400

Total

Small Amount

170

20

190

Medium Amount

100

40

140

Large Amount

65

5

335

65

70 400

Total 83.75%'of'sampled'invoices'have'no' errors'and'47.50%'of'sampled' invoices' are'for'small'amounts.

No Errors

Errors

Total

Small Amount

42.50%

5.00%

47.50%

Medium Amount

25.00%

10.00%

35.00%

Large Amount

16.25%

1.25%

17.50%

Total

83.75%

16.25%

100.0%

DCOVA'– Categorical'Data ! Contingency'tables'with'%'of'row'total' No Errors

Errors

89.47%'='170'/'190 71.43%'='100'/'140 92.86%'='''65'/'70

Total

Small Amount

170

20

190

Medium Amount

100

40

140

Large Amount

65

5

335

65

Total Medium'invoices'have'a'larger'chance' (28.57%)'of'having'errors'than'small' (10.53%)'or'large'(7.14%)'invoices.

70 400

No Errors

Errors

Total

Small Amount

89.47%

10.53%

100.0%

Medium Amount

71.43%

28.57%

100.0%

Large Amount

92.86%

7.14%

100.0%

Total

83.75%

16.25%

100.0%

DCOVA'– Categorical'Data ! Contingency'tables'with'%'of'column'total' No Errors

Errors

50.75%'='170'/'335 30.77%'='''20'/'65

Total

Small Amount

170

20

190

Medium Amount

100

40

140

Large Amount

65

Total

335

5

No Errors

Errors

Total

Small Amount

50.75%

30.77%

47.50%

Medium Amount

29.85%

61.54%

35.00%

Large Amount

19.40%

7.69%

17.50%

Total

100.0%

100.0%

100.0%

70

65

400

There'is'a'61.54%'chance'that'invoices' with'errors'are'of'medium'size.

DCOVA'– Numerical'Data Numerical-Data

Ordered-Array

Frequency Distributions

Cumulative Distributions

Chap'2740 Chap'2740

DCOVA'– Numerical'Data ! Ordered'array ! Sequence'of'data,'in'rank'order,'from'the'smallest'value'to'the' largest'value ! Shows'range'(minimum' value'to'maximum'value) ! May'help'identify'outliers'(unusual'observations) Age-ofSurveyedCollegeStudents

Day-Students 16

17

17

18

18

18

19

19

20

20

21

22

22

25

27

32

38

42

Night-Students 18

18

19

19

20

21

23

28

32

33

41

45 41

DCOVA'– Numerical'Data ! Frequency'distribution ! summary' table'in'which'the'data'are'arranged'into'numerically' ordered'classes.

! Important: ! Select'the'appropriate'number'of'class-groupings-for'the'table,' determine' a'suitable'width'of'a'class'grouping,'and'establish'the' boundaries'of'each'class'grouping'to'avoid'overlapping. ! The'number'of'classes'depends'on'the'number'of'values'in'the' data. ! With'a'larger'number'of'values,'typically'there'are'more'classes ! General'rule:'at'least'5'but'no'more'than'15'classes.

! To'determine' the'width-of-a-class-interval,-divide'the'range(Highest'value–Lowest' value)'of'the'data'by'the'number'of'class' groupings'desired.' 42

DCOVA'– Numerical'Data ! E.g.'frequency'distribution ! A'manufacturer'of'insulation'randomly'selects'20' winter'days'and'records'the'daily'high' temperature

! Data ! 24,'35,'17,'21,'24,'37,'26,'46,'58,'30,'32,'13,'12,' 38,'41,'43,'44,'27,'53,'27

43

DCOVA'– Numerical'Data ! Sort'raw'data'in'ascending'order:'12,-13,-17,-21,-24,-24,26,-27,-27,-30,-32,-35,-37,-38,-41,-43,-44,-46,-53,-58 ! Find'range:'58-\ 12-=-46 ! Select'number'of'classes:'5-(usually-between-5-and-15) ! Compute'class'interval'(width):'10-(46/5-then-round-up) ! Determine'class'boundaries'(limits): ! ! ! ! !

Class'1:''10'to'less'than'20 Class'2:''20'to'less'than'30 Class'3:''30'to'less'than'40 Class'4:''40'to'less'than'50 Class'5:''50'to'less'than'60

! Compute'class'midpoints:'15,-25,-35,-45,--55 ! Count'observations'&'assign'to'classes

44

Frequency'Distribution'Example Data-in-ordered-array:

12,-13,-17,-21,-24,-24,-26,-27,-27,-30,-32,-35,-37,-38,-41,-43,-44,-46,-53,-58

Class---------------------------

Midpoints

Frequency

10-but-less-than-20-------------------15 20-but-less-than-30-------------------25 30-but-less-than-40-------------------35 40-but-less-than-50-------------------45 50-but-less-than-60-------------------55 Total

3 6 5-------------4 2------------20

Chap'2745 Chap'2745

Relative'and'Percent'Frequency'Dn Data-in-ordered-array:

12,-13,-17,-21,-24,-24,-26,-27,-27,-30,-32,-35,-37,-38,-41,-43,-44,-46,-53,-58

Class--------------------------

Frequency

Relative Frequency

Percentage

10-but-less-than-20-------------------3----------------- .15-----------------------15 20-but-less-than-30-------------------6------------------ .30-----------------------30 30-but-less-than-40-------------------5------------------ .25-----------------------25-------------40-but-less-than-50-------------------4------------------ .20----------------------- 20 50-but-less-than-60-------------------2----------------- .10-----------------------10------------Total 20---------------1.00---------------------100 Chap'2746 Chap'2746

Cumulative'Frequency'Distribution Data-in-ordered-array:

12,-13,-17,-21,-24,-24,-26,-27,-27,-30,-32,-35,-37,-38,-41,-43,-44,-46,-53,-58

Class

Frequency

Percentage

CumulativeFrequency

CumulativePercentage

10-but-less-than-20

3-----------------

15%-----------------3------------------- 15%

20-but-less-than-30

6-----------------

30%-----------------9------------------ 45%

30-but-less-than-40

5----------------

25%---------------14-------------------70%

40-but-less-than-50

4---------------

20%---------------18-------------------90%

50-but-less-than-60

2-----------------

10%---------------20---------------- 100%

Total

20-----------------100

20

100%

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Chap'2747

Chap'2...