IS 310 Business Statistics CSU Long Beach

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IS 310 – Business Statistics IS 310 – Business Statistics

IS 310

Business Statistic

sCSU

Long Beach

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Why Study Statistics?Why Study Statistics?

Because, you would like to Because, you would like to know:know:

1.1.How does an instructor How does an instructor grade on a curvegrade on a curve2.2.How does a tire How does a tire manufacturer determine manufacturer determine mileage warrantymileage warranty3.3.How does FDA verify that a How does FDA verify that a new drug is more effective new drug is more effective than the present drugthan the present drug4.4.What does it mean when one What does it mean when one says the median home price in says the median home price in southern California is $420,000southern California is $420,0005.5.How does one select a How does one select a sample for a surveysample for a survey

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What is Statistics?What is Statistics?

Statistics is a field of study that deals Statistics is a field of study that deals with with collection, organization, collection, organization, presentation, analysis and presentation, analysis and interpretation of datainterpretation of data..

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Applications in Applications in Business and EconomicsBusiness and Economics

AccountingAccounting

EconomicsEconomics

Public accounting firms use statisticalPublic accounting firms use statistical

sampling procedures when conductingsampling procedures when conducting

audits for their clients.audits for their clients.

Economists use statistical informationEconomists use statistical information

in making forecasts about the future ofin making forecasts about the future of

the economy or some aspect of it.the economy or some aspect of it.

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A variety of statistical quality A variety of statistical quality

control charts are used to monitorcontrol charts are used to monitor

the output of a production process.the output of a production process.

ProductionProduction

Electronic point-of-sale scanners atElectronic point-of-sale scanners at

retail checkout counters are used toretail checkout counters are used to

collect data for a variety of marketingcollect data for a variety of marketing

research applications.research applications.

MarketingMarketing

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Financial advisors use price-earnings ratios andFinancial advisors use price-earnings ratios and

dividend yields to guide their investmentdividend yields to guide their investment

recommendations.recommendations.

FinanceFinance

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Data and Data SetsData and Data Sets

DataData are the facts and figures collected, summarized, are the facts and figures collected, summarized, analyzed, and interpreted.analyzed, and interpreted.

The data collected in a particular study are referredThe data collected in a particular study are referred to as the to as the data setdata set..

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The The elementselements are the entities on which data are are the entities on which data are collected.collected. A A variablevariable is a characteristic of interest for the elements. is a characteristic of interest for the elements.

The set of measurements collected for a particularThe set of measurements collected for a particular element is called an element is called an observationobservation..

The total number of data values in a complete dataThe total number of data values in a complete data set is the number of elements multiplied by theset is the number of elements multiplied by the number of variables.number of variables.

Elements, Variables, and ObservationsElements, Variables, and Observations

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Stock Annual Earn/Stock Annual Earn/Exchange Sales($M) Share($)Exchange Sales($M) Share($)

Data, Data Sets, Data, Data Sets, Elements, Variables, and ObservationsElements, Variables, and Observations

CompanyCompany

DataramDataram

EnergySouthEnergySouth

KeystoneKeystone

LandCareLandCare

PsychemedicsPsychemedics

NQNQ 73.10 73.10 0.86 0.86

NN 74.00 74.00 1.67 1.67

NN 365.70365.70 0.86 0.86

NQNQ 111.40111.40 0.33 0.33

NN 17.60 17.60 0.13 0.13

VariableVariablessElemenElemen

tt NamesNames

Data SetData Set

ObservatioObservationn

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Scales of MeasurementScales of Measurement

The scale indicates the data summarization andThe scale indicates the data summarization and statistical analyses that are most appropriate.statistical analyses that are most appropriate. The scale indicates the data summarization andThe scale indicates the data summarization and statistical analyses that are most appropriate.statistical analyses that are most appropriate.

The scale determines the amount of informationThe scale determines the amount of information contained in the data.contained in the data. The scale determines the amount of informationThe scale determines the amount of information contained in the data.contained in the data.

Scales of measurement include:Scales of measurement include: Scales of measurement include:Scales of measurement include:

NominalNominal

OrdinalOrdinal

IntervalInterval

RatioRatio

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NominalNominal

A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used. A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used.

Data are Data are labels or nameslabels or names used to identify an used to identify an attribute of the element.attribute of the element. Data are Data are labels or nameslabels or names used to identify an used to identify an attribute of the element.attribute of the element.

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Example:Example: Students of a university are classified by theStudents of a university are classified by the school in which they are enrolled using aschool in which they are enrolled using a nonnumeric label such as Business, Humanities,nonnumeric label such as Business, Humanities, Education, and so on.Education, and so on.

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business,the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and2 denotes Humanities, 3 denotes Education, and so on).so on).

Example:Example: Students of a university are classified by theStudents of a university are classified by the school in which they are enrolled using aschool in which they are enrolled using a nonnumeric label such as Business, Humanities,nonnumeric label such as Business, Humanities, Education, and so on.Education, and so on.

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business,the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and2 denotes Humanities, 3 denotes Education, and so on).so on).


NominalNominal

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OrdinalOrdinal

A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used. A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used.

The data have the properties of nominal data andThe data have the properties of nominal data and the the order or rank of the data is meaningfulorder or rank of the data is meaningful.. The data have the properties of nominal data andThe data have the properties of nominal data and the the order or rank of the data is meaningfulorder or rank of the data is meaningful..

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OrdinalOrdinal

Example:Example: Students of a university are classified by theirStudents of a university are classified by their class standing using a nonnumeric label such as class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.Freshman, Sophomore, Junior, or Senior.

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used for the class standing variable (e.g. 1 denotesthe class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).Freshman, 2 denotes Sophomore, and so on).

Example:Example: Students of a university are classified by theirStudents of a university are classified by their class standing using a nonnumeric label such as class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.Freshman, Sophomore, Junior, or Senior.

Alternatively, a numeric code could be used forAlternatively, a numeric code could be used for the class standing variable (e.g. 1 denotesthe class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).Freshman, 2 denotes Sophomore, and so on).

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IntervalInterval

Interval data are Interval data are always numericalways numeric.. Interval data are Interval data are always numericalways numeric..

The data have the properties of ordinal data, andThe data have the properties of ordinal data, and the interval between observations is expressed inthe interval between observations is expressed in terms of a fixed unit of measure.terms of a fixed unit of measure.

The data have the properties of ordinal data, andThe data have the properties of ordinal data, and the interval between observations is expressed inthe interval between observations is expressed in terms of a fixed unit of measure.terms of a fixed unit of measure.

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IntervalInterval

Example:Example: Melissa has an SAT score of 1205, while KevinMelissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115has an SAT score of 1090. Melissa scored 115 points more than Kevin.points more than Kevin.

Example:Example: Melissa has an SAT score of 1205, while KevinMelissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115has an SAT score of 1090. Melissa scored 115 points more than Kevin.points more than Kevin.

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RatioRatio

The data have all the properties of interval dataThe data have all the properties of interval data and the and the ratio of two values is meaningfulratio of two values is meaningful.. The data have all the properties of interval dataThe data have all the properties of interval data and the and the ratio of two values is meaningfulratio of two values is meaningful..

Variables such as distance, height, weight, and timeVariables such as distance, height, weight, and time use the ratio scale.use the ratio scale. Variables such as distance, height, weight, and timeVariables such as distance, height, weight, and time use the ratio scale.use the ratio scale.

This This scale must contain a zero valuescale must contain a zero value that indicates that indicates that nothing exists for the variable at the zero point.that nothing exists for the variable at the zero point. This This scale must contain a zero valuescale must contain a zero value that indicates that indicates that nothing exists for the variable at the zero point.that nothing exists for the variable at the zero point.

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RatioRatio

Example:Example: Melissa’s college record shows 36 credit hoursMelissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credithours earned. Kevin has twice as many credit hours earned as Melissa.hours earned as Melissa.

Example:Example: Melissa’s college record shows 36 credit hoursMelissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credithours earned. Kevin has twice as many credit hours earned as Melissa.hours earned as Melissa.

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Data can be further classified as being qualitativeData can be further classified as being qualitative or quantitative.or quantitative. Data can be further classified as being qualitativeData can be further classified as being qualitative or quantitative.or quantitative.

The statistical analysis that is appropriate dependsThe statistical analysis that is appropriate depends on whether the data for the variable are qualitativeon whether the data for the variable are qualitative or quantitative.or quantitative.

The statistical analysis that is appropriate dependsThe statistical analysis that is appropriate depends on whether the data for the variable are qualitativeon whether the data for the variable are qualitative or quantitative.or quantitative.

In general, there are more alternatives for statisticalIn general, there are more alternatives for statistical analysis when the data are quantitative.analysis when the data are quantitative. In general, there are more alternatives for statisticalIn general, there are more alternatives for statistical analysis when the data are quantitative.analysis when the data are quantitative.

Qualitative and Quantitative DataQualitative and Quantitative Data

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Qualitative DataQualitative Data

Labels or namesLabels or names used to identify an attribute of each used to identify an attribute of each elementelement Labels or namesLabels or names used to identify an attribute of each used to identify an attribute of each elementelement

Often referred to as Often referred to as categorical datacategorical data Often referred to as Often referred to as categorical datacategorical data

Use either the nominal or ordinal scale ofUse either the nominal or ordinal scale of measurementmeasurement Use either the nominal or ordinal scale ofUse either the nominal or ordinal scale of measurementmeasurement

Can be either numeric or nonnumericCan be either numeric or nonnumeric Can be either numeric or nonnumericCan be either numeric or nonnumeric

Appropriate statistical analyses are rather limitedAppropriate statistical analyses are rather limited Appropriate statistical analyses are rather limitedAppropriate statistical analyses are rather limited

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Quantitative DataQuantitative Data

Quantitative data indicate Quantitative data indicate how many or how much:how many or how much: Quantitative data indicate Quantitative data indicate how many or how much:how many or how much:

discretediscrete, if measuring how many, if measuring how many discretediscrete, if measuring how many, if measuring how many

continuouscontinuous, if measuring how much, if measuring how much continuouscontinuous, if measuring how much, if measuring how much

Quantitative data are Quantitative data are always numericalways numeric.. Quantitative data are Quantitative data are always numericalways numeric..

Ordinary arithmetic operations are meaningful forOrdinary arithmetic operations are meaningful for quantitative data.quantitative data. Ordinary arithmetic operations are meaningful forOrdinary arithmetic operations are meaningful for quantitative data.quantitative data.

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QualitativeQualitativeQualitativeQualitative QuantitativQuantitativee

QuantitativQuantitativee

NumericalNumericalNumericalNumerical NumericalNumericalNumericalNumericalNon-Non-numericalnumerical

Non-Non-numericalnumerical

DataDataDataData

NominaNominallNominaNominall

OrdinaOrdinallOrdinaOrdinall

NominalNominalNominalNominal OrdinalOrdinalOrdinalOrdinal IntervalIntervalIntervalInterval RatioRatioRatioRatio

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Cross-Sectional DataCross-Sectional Data

Cross-sectional dataCross-sectional data are collected at the same or are collected at the same or approximately the same point in time.approximately the same point in time. Cross-sectional dataCross-sectional data are collected at the same or are collected at the same or approximately the same point in time.approximately the same point in time.

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in June 2007 in each of the countiespermits issued in June 2007 in each of the counties of Ohioof Ohio

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in June 2007 in each of the countiespermits issued in June 2007 in each of the counties of Ohioof Ohio

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Time Series DataTime Series Data

Time series dataTime series data are collected over several time are collected over several time periods.periods. Time series dataTime series data are collected over several time are collected over several time periods.periods.

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in Lucas County, Ohio in each ofpermits issued in Lucas County, Ohio in each of the last 36 monthsthe last 36 months

ExampleExample: data detailing the number of building: data detailing the number of building permits issued in Lucas County, Ohio in each ofpermits issued in Lucas County, Ohio in each of the last 36 monthsthe last 36 months

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Data SourcesData Sources

Existing SourcesExisting Sources

Within a firmWithin a firm – almost any department – almost any department

Business database servicesBusiness database services – Dow Jones & Co. – Dow Jones & Co.

Government agenciesGovernment agencies - U.S. Department of Labor - U.S. Department of Labor

Industry associationsIndustry associations – Travel Industry Association – Travel Industry Association of Americaof America

Special-interest organizationsSpecial-interest organizations – Graduate Management – Graduate Management Admission CouncilAdmission Council

InternetInternet – more and more firms – more and more firms

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Statistical StudiesStatistical Studies

Data SourcesData Sources

In In experimental studiesexperimental studies the variable of interest is the variable of interest isfirst identified. Then one or more other variablesfirst identified. Then one or more other variablesare identified and controlled so that data can beare identified and controlled so that data can beobtained about how they influence the variable ofobtained about how they influence the variable ofinterest.interest.

In In experimental studiesexperimental studies the variable of interest is the variable of interest isfirst identified. Then one or more other variablesfirst identified. Then one or more other variablesare identified and controlled so that data can beare identified and controlled so that data can beobtained about how they influence the variable ofobtained about how they influence the variable ofinterest.interest.

In In observationalobservational (nonexperimental) (nonexperimental) studiesstudies no no attempt is made to control or influence theattempt is made to control or influence the variables of interest.variables of interest.

In In observationalobservational (nonexperimental) (nonexperimental) studiesstudies no no attempt is made to control or influence theattempt is made to control or influence the variables of interest.variables of interest. a a surveysurvey is a good is a good

exampleexamplea a surveysurvey is a good is a good

exampleexample

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Data Acquisition ConsiderationsData Acquisition Considerations

Time RequirementTime RequirementTime RequirementTime Requirement

Cost of AcquisitionCost of AcquisitionCost of AcquisitionCost of Acquisition

Data ErrorsData Errors Data ErrorsData Errors

• Searching for information can be time consuming.Searching for information can be time consuming.• Information may no longer be useful by the time itInformation may no longer be useful by the time it is available.is available.

• Organizations often charge for information evenOrganizations often charge for information even when it is not their primary business activity.when it is not their primary business activity.

• Using any data that happen to be available or wereUsing any data that happen to be available or were acquired with little care can lead to misleadingacquired with little care can lead to misleading information.information.

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Descriptive StatisticsDescriptive Statistics

Descriptive statisticsDescriptive statistics are the tabular, are the tabular, graphical, and numerical methods used to graphical, and numerical methods used to summarize and presentsummarize and present data. data.

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Example: Hudson Auto RepairExample: Hudson Auto Repair

The manager of Hudson AutoThe manager of Hudson Auto

would like to have a betterwould like to have a better

understanding of the costunderstanding of the cost

of parts used in the engineof parts used in the engine

tune-ups performed in thetune-ups performed in the

shop. She examines 50shop. She examines 50

customer invoices for tune-ups. The costs of customer invoices for tune-ups. The costs of parts,parts,

rounded to the nearest dollar, are listed on the rounded to the nearest dollar, are listed on the nextnext

slide.slide.

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Example: Hudson Auto RepairExample: Hudson Auto Repair

Sample of Parts Cost ($) for 50 Tune-Sample of Parts Cost ($) for 50 Tune-upsups

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

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Inferential StatisticsInferential Statistics

Inferential Statistics Inferential Statistics involves analyzing a set of involves analyzing a set of data to make conclusions. This branch of data to make conclusions. This branch of statistics is more difficult than Descriptive statistics is more difficult than Descriptive Statistics.Statistics.

In the study of Inferential Statistics, two basic In the study of Inferential Statistics, two basic concepts are important:concepts are important:

o Populationo Population

o Sampleo Sample

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Population and SamplePopulation and Sample

Population refers to all possible subjects Population refers to all possible subjects for a given study.for a given study.

Sample refers to part (subset) of a Sample refers to part (subset) of a population.population.

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Let’s take a few examples.Let’s take a few examples. Example 1Example 1 We are interested in knowing the proportion of We are interested in knowing the proportion of

CSULB students are in favor of legalizing the CSULB students are in favor of legalizing the use of marijuana.use of marijuana.

Population consists of Population consists of allall CSULB students. CSULB students.

Sample is 250 students selected at random.Sample is 250 students selected at random.

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Example 2Example 2 We want to know what percentage of Los We want to know what percentage of Los

Angeles County residents are supportive of a Angeles County residents are supportive of a half-percent increase in sales tax.half-percent increase in sales tax.

Population consists of Population consists of allall Los Angeles County Los Angeles County residents who are at least 18 years old.residents who are at least 18 years old.

Sample is 1000 Los Angeles County residents Sample is 1000 Los Angeles County residents selected randomly.selected randomly.

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Example 3Example 3 We want to test if a new brand of tires We want to test if a new brand of tires

manufactured by Goodyear is better than manufactured by Goodyear is better than existing tires.existing tires.

Population consists of Population consists of allall tires of the new tires of the new brand manufactured by Goodyear.brand manufactured by Goodyear.

Sample is 100 tires of the new brand chosen at Sample is 100 tires of the new brand chosen at random.random.

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Example 4Example 4

We would like to know if a new perfume will be We would like to know if a new perfume will be preferred by American women over 35 years.preferred by American women over 35 years.

Population consists of Population consists of allall American women American women who are over 35 years.who are over 35 years.

Sample is 500 American women of over 35 Sample is 500 American women of over 35 years selected randomly.years selected randomly.

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Example 5Example 5

A restaurant has undergone extensive A restaurant has undergone extensive remodeling and wants to know if customers remodeling and wants to know if customers will like the new décor. will like the new décor.

Population consists of Population consists of all all customers who have customers who have visited the restaurant in the past.visited the restaurant in the past.

Sample consists of customers who visited the Sample consists of customers who visited the restaurant during a specific month. restaurant during a specific month.

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Example 6Example 6

American Airlines is planning to introduce a American Airlines is planning to introduce a new policy on flying hours by its pilots.new policy on flying hours by its pilots.

Population consists of Population consists of allall American Airlines American Airlines pilots.pilots.

Sample consists of 50 American Airlines pilots Sample consists of 50 American Airlines pilots selected at random.selected at random.

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Example 7Example 7

A workers union has reached a new contract A workers union has reached a new contract with management. It wants to know the opinion with management. It wants to know the opinion of its members on the terms and conditions of of its members on the terms and conditions of the new contract.the new contract.

Population consists of Population consists of allall members of the union. members of the union.

Sample consists of 50 union members selected Sample consists of 50 union members selected at random.at random.

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Example 8Example 8

FDA wants to compare the average nicotine content of FDA wants to compare the average nicotine content of two brands of cigarettes: Brand A and Brand B.two brands of cigarettes: Brand A and Brand B.

There are two populations: There are two populations: allall cigarettes of Brand A and cigarettes of Brand A and allall cigarettes of Brand B. cigarettes of Brand B.

Sample A consists of 100 cigarettes chosen randomly Sample A consists of 100 cigarettes chosen randomly from all Brand A cigarettes.from all Brand A cigarettes.

Sample B consists of 100 cigarettes chosen randomly Sample B consists of 100 cigarettes chosen randomly from all Brand B cigarettes.from all Brand B cigarettes.

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Population and Sample Population and Sample

Example 9Example 9

You want to compare home prices between You want to compare home prices between Costa Mesa and Fountain Valley.Costa Mesa and Fountain Valley.

There are two populations: Population A consists There are two populations: Population A consists of of allall homes in Costa Mesa. Population B homes in Costa Mesa. Population B consists of consists of allall homes in Fountain Valley. homes in Fountain Valley.

Sample A consists of 100 homes selected at Sample A consists of 100 homes selected at random from all homes in Costa Mesa. Sample B random from all homes in Costa Mesa. Sample B consists of 100 homes from all homes in consists of 100 homes from all homes in Fountain Valley.Fountain Valley.

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Example 10Example 10

A research firm wants to compare the average fat content A research firm wants to compare the average fat content used in meat between McDonald’s Big Mac and Burger used in meat between McDonald’s Big Mac and Burger King’s Whopper during the month of September in Los King’s Whopper during the month of September in Los Angeles county.Angeles county.

There are two populations: Population A consists of There are two populations: Population A consists of allall Big Big Macs made by McDonald in the month of September in Los Macs made by McDonald in the month of September in Los Angeles County. Population B consists of Angeles County. Population B consists of allall Whoppers Whoppers made by Burger King in September in Los Angeles County.made by Burger King in September in Los Angeles County.

Sample A consists of 200 Big Macs selected randomly from Sample A consists of 200 Big Macs selected randomly from Population A and Sample B consists of 200 Whoppers Population A and Sample B consists of 200 Whoppers selected at random from Population B.selected at random from Population B.

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More on Population and SampleMore on Population and Sample

Answer if the following questions deal with population Answer if the following questions deal with population or sample.or sample.

What is the average MPG of cars driven by all CSULB What is the average MPG of cars driven by all CSULB students?students?

What percent of 500 students selected at random What percent of 500 students selected at random support off-shore drilling for oil?support off-shore drilling for oil?

What is the range of income of all residents of Long What is the range of income of all residents of Long Beach?Beach?

What is the average weight of chickens raised in a What is the average weight of chickens raised in a farm?farm?

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Sample ProblemsSample Problems

Problem # 11 on page 21Problem # 11 on page 21

A. Annual sales – Quantitative and ratio.A. Annual sales – Quantitative and ratio. B. Soft drink size – Qualitative and ordinal.B. Soft drink size – Qualitative and ordinal. C. Employee classification – Qualitative and C. Employee classification – Qualitative and

nominal.nominal. D. Earnings per share – Quantitative and ratio.D. Earnings per share – Quantitative and ratio. E. Method of payment – Qualitative and E. Method of payment – Qualitative and

nominal.nominal.

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Sample ProblemsSample Problems

Problem # 22 on page 24Problem # 22 on page 24

A. All registered voters in California.A. All registered voters in California. B. Those registered voters who were B. Those registered voters who were

contacted by the policy Institute of California.contacted by the policy Institute of California. C. A sample was reduced to reduce the cost C. A sample was reduced to reduce the cost

and time.and time.

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Statistical InferenceStatistical Inference

Statistical inference is a statistical procedure to Statistical inference is a statistical procedure to determine the characteristics of a population by determine the characteristics of a population by studying a sample.studying a sample.

Let’s the case of Norris Electronics mentioned in Let’s the case of Norris Electronics mentioned in your book. Norris developed a new light bulb that your book. Norris developed a new light bulb that increases its useful life. In this case, all new light increases its useful life. In this case, all new light bulbs comprise the population. To test if the new bulbs comprise the population. To test if the new light bulb really has a longer life, a sample of 200 light bulb really has a longer life, a sample of 200 bulbs was tested and the average life of these bulbs was tested and the average life of these bulbs was calculated. This average life will be used bulbs was calculated. This average life will be used to conclude if the new bulb has a longer useful life. to conclude if the new bulb has a longer useful life. This is an example of statistical inference. This is an example of statistical inference.

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Statistical InferenceStatistical Inference

Statistical inference allows us to make Statistical inference allows us to make conclusions about a population. This conclusion conclusions about a population. This conclusion is made by studying a sample.is made by studying a sample.

In the Norris case, the population was all new In the Norris case, the population was all new light bulbs whose life expectancy we wanted to light bulbs whose life expectancy we wanted to verify. verify.

Do all the new bulbs have a longer life?Do all the new bulbs have a longer life? We answered this question by studying a We answered this question by studying a

sample and calculating the average life of this sample and calculating the average life of this sample of bulbs.sample of bulbs.

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End of Chapter 1End of Chapter 1

IS 310 Business Statistics CSU Long Beach

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