book

Statistics for Business: Decision Making and Analysis, 3rd Edition

by Robert Stine, Dean Foster

January 2017

Beginner

882 pages

203h 41m

English

Pearson

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What’s New in This EditionCoverage and OrganizationFeatures
Instructor ResourcesTechnology Resources

Chapter 1 Introduction
VariationPatterns and Models
Predicting EmploymentPricing a Car
Running a Business is Hard Work.
Rows and Columns
Measurement ScalesWhat Do You Think?
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Sources of DataMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesAbout the Data
Mix and MatchTrue/FalseThink About It
Consumers Spend Billions of Dollars Online.
VariationFrequency Table
Bar ChartPie ChartWhat Do You Think?
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
A Standard iPhone 6 Comes with 16 Gigabytes (GB) of Memory.
PercentilesWhat Do You Think?AveragesMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsWhat Do You Think?
Histograms versus Bar ChartsThe White Space RuleWidth of Histogram Intervals
Combining Boxplots with HistogramsWhat Do You Think?
ModesSymmetry and SkewnessMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsWhat Do You Think?Bell-Shaped Distributions and the Empirical RuleStandardizingWhat Do You Think?
Key TermsObjectivesFormulasMean (Average)VarianceStandard Deviation (SD)Z-ScoreCoefficient of VariationAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Busy Web Sites Charge for Running Ads on Their Pages.
Marginal and Conditional DistributionsWhat Do You Think?Stacked Bar ChartsMosaic PlotsMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsWhat Do You Think?
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Chi-SquaredWhat Do You Think?Cramer’s VMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasChi-SquaredCramer’s VAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
What Does It Cost To Heat a Home for the Winter?
Visual Test for AssociationWhat Do You Think?Describing Association in a ScatterplotWhat Do You Think?
CovarianceCorrelationWhat Do You Think?
Slope-Intercept FormLines and PredictionNonlinear Patterns
What Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasCovarianceCorrelationExpressions Relating Covariance and CorrelationCorrelation LineAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Stock PricesSome Details: Stock Splits
Simple Time SeriesHistograms
Return on an Investment
Utility for WealthLogs and Histograms
Chapter 7 ProbabilityThousands of Customers Dial Toll-Free Telephone Numbers to Get Help.
The Law of Large NumbersWhat Do You Think?
Three Essential RulesThe Complement and Addition RulesAn ExampleWhat Do You Think?
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsBoole’s Inequality
Key TermsObjectivesFormulas and NotationComplement of an EventUnion of EventsIntersection of EventsBoole’s Inequality
Mix and MatchTrue/FalseThink About ItYou Do It
Education Affects the Income That You Can Expect to Earn.
Joint ProbabilityMarginal ProbabilityConditional ProbabilityWhat Do You Think?What Do You Think?
The Multiplication RuleWhat Do You Think?Order MattersIndependence in Venn DiagramsWhat Do You Think?
Probability TreesProbability Tables
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsBayes’ RuleMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasConditional ProbabilityMultiplication RuleBayes’ RuleAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Day Trading Is Popular with Young People Around the World.
Graphs of Random VariablesRandom Variables as ModelsWhat Do You Think?
Mean of a Random VariableExpected ValueWhat Do You Think?Variance and Standard DeviationMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Adding or Subtracting a ConstantMultiplying by a ConstantWhat Do You Think?
Sharpe Ratio
Key TermsObjectivesFormulasMean or Expected Value of a Discrete Random Variable XVariance of a Discrete Random VariableAdding a Constant to a Random VariableMultiplying a Random Variable by a ConstantAdding a Constant and Multiplying by a ConstantSharpe Ratio of the Random Variable X with Mean μ and Variance σ2About the Data
Mix and MatchTrue/FalseThink About ItYou Do It
The Two Largest Stock Exchanges in the World
Two Random VariablesComparisons and the Sharpe Ratio
Independent Random VariablesWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsDependent Random Variables
What Do You Think?
CovarianceCovariance and SumsCorrelationCovariance, Correlation, and Independence
IID DataWhat Do You Think?
Variance of DifferencesMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasJoint Probability Distribution of Two Random VariablesMultiplication Rule for Expected Values.Addition Rule for Expected Values of SumsAddition Rule for Variances of SumsCovariance Between Random VariablesCorrelation Between Random VariablesAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Pharmaceutical Advertising Appears On Television,
Bernoulli Random VariableCounting SuccessesWhat Do You Think?
AssumptionsFinite Populations
Mean and VarianceBinomial ProbabilitiesSummaryWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Poisson Random VariablePoisson ModelMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasBinomial Random Variable, Y ~ Bi(n, p)Poisson Random Variable, X ~ Poisson (λ)
Mix and MatchTrue/FalseThink About ItYou Do It
Prices of Stock Plummeted in October 1987.
Central Limit TheoremNormal Probability DistributionShifts and Scales
What Do You Think?StandardizingThe Empirical Rule, RevisitedMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsUsing Normal TablesWhat Do You Think?
What Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Normal Quantile PlotSkewness and Kurtosis
Key TermsObjectivesFormulasProbability DistributionSkewnessKurtosisAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Dice InvestmentsSimulationA Two-Investment Portfolio
Random VariablesProperties of a PortfolioVolatility Drag
Broader Implications
A Model for CountsUsing the Model
Counting Possibilities
Weighing in Place of CountingUsing NormalityDoes It Matter?
Chapter 13 Samples and SurveysThe Claim “Ranked Tops in Initial Quality” Often Appears in Advertisements for New Cars.
RandomizationSample SizeWhat Do You Think?Simple Random SampleIdentifying the Sampling FrameWhat Do You Think?
Estimating ParametersSampling VariationMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Stratified and Cluster SamplesMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsCensusVoluntary ResponseConvenience SamplesWhat Do You Think?
Key TermsObjectivesAbout the Data
Mix and MatchTrue/FalseThink About It
Delivery Services Love GPS Devices.
Benefits of AveragingNormal ModelsWhat Do You Think?Standard Error of the MeanSampling DistributionWhat Do You Think?
Type I and Type II ErrorsWhat Do You Think?Setting the Control LimitsBalancing Type I and Type II ErrorsWhat Do You Think?
Repeated TestingRecognizing a Problem
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasSampling DistributionStandard Error of the MeanSample Size ConditionUpper and Lower Control LimitsAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
The Federal Reserve Says That U.S. Households Have Accumulated Close to $12 Trillion in Outstanding Debt.
Confidence Interval for the ProportionWhat Do You Think?ChecklistAssumptions and ConditionsSample SizeWhat Do You Think?
Student’s t-Distributiont-Interval for the MeanChecklistWhat Do You Think?
Common Confusions
Combining Confidence IntervalsChanging the ProblemWhat Do You Think?
Determining Sample SizeWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasz-Interval for the Proportiont-Interval for the MeanMargin of ErrorAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Spam Is Annoying. Junk Email Takes Time to Delete, and You Sometimes Mistakenly Throw Out Messages You Want Along with the Junk.
Null and Alternative HypothesesWhat Do You Think?Type I and II ErrorsPrevious Hypothesis TestsWhat Do You Think?Test StatisticWhat Do You Think?
α Levelz-TestWhat Do You Think?p-ValueType II ErrorSummaryMotivation State The QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize The Results
t-Statistict-Test and p-ValueSummaryMotivation State the QuestionMethod Describe The Data and Select an ApproachMechanics Do The AnalysisMessage Summarize The Results
Key TermsObjectivesFormulasOne-Sided z-Test of a ProportionOne-Sided t-Test of a MeanAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Diets Are Big Business.
ExperimentsConfoundingWhat Do You Think?
Interpreting the Confidence IntervalChecklistWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
What Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize The Results
Interpreting the Confidence IntervalChecklist (see the two-sample t-test)Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
ChecklistMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasStandard Error of the Difference Between Two Sample MeansTwo-Sample t-Test for the Difference in MeansTwo-Sample Confidence Interval for the Difference in MeansAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Online Marketing Allows a Retailer to Customize Sales Pitches.
Hypotheses for the chi-squared testWhat Do You Think?Calculating χ2What Do You Think?Plots of the Chi-Squared Test of IndependenceConditionsThe Chi-Squared DistributionGetting the p-ValueSummary: Chi-Squared Test of IndependenceConnection to Two-Sample TestsWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Testing for RandomnessMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsTesting the Fit of a Probability ModelMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasDegrees of Freedom (d)Chi-Squared StatisticAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Clinical TrialsDefaults on Corporate BondsElectronic Components
Rule of ThreeUsing the Rule of ThreeDetermining nConsiderations in Finance
Looking for AssociationChi-squared Test of AssociationEquality of Several Proportions
Standardizing with p-valuesRelated Methods
Chapter 19 Linear PatternsMany Factors Affect the Price of a Commodity.
Equation of a LineLeast Squares
Interpreting the InterceptInterpreting the SlopeWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsWhat Do You Think?
Standard Deviation of the Residuals
Summarizing the Fit of a Line
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasLinear EquationSlopeInterceptFitted ValueResidualStandard Deviation of the Residualsr-squaredAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
The Price of Gasoline Can Be a Painful Reminder of the Laws of Supply and Demand.
ScatterplotsResidual Plots
What Do You Think?Comparing Linear and Nonlinear EquationsVisual ComparisonsSubstantive ComparisonWhat Do You Think?
Scatterplots and Residual PlotsComparing EquationsElasticityMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Customized Manufacturing Is a Growth Industry in the United States As Businesses Adjust to Worldwide Competition.
Linear on AverageDeviations from the MeanData-Generating ProcessWhat Do You Think?
Modeling ProcessWhat Do You Think?
Standard ErrorsRole of SoftwareConfidence IntervalsHypothesis TestsWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Leveraging the SRMReliability of Prediction IntervalsMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasSimple Regression ModelChecklist of Conditions for the Simple Regression ModelStandard Error of the SlopeStandard Error of the InterceptStandard Error of PredictionAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
The Internet Has Changed Many Business Models, Generating New Approaches to Retail Marketing, Medical Care, and Service Industries.
Fixed Costs, Marginal Costs, and Variable CostsDetecting Differences in VariationConsequences of Different VariationWhat Do You Think?Fixing the Problem: Revise the ModelMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsComparing Models with Different Responses
Consequences of an OutlierWhat Do You Think?Extrapolating Prediction IntervalsFixing the Problem: More Information
Detecting Dependence Using the Durbin-Watson StatisticConsequences of DependenceMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasDurbin-Watson StatisticAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Expanding Businesses Must Decide Where to Locate New Outlets.
What Do You Think?
Scatterplot MatrixWhat Do You Think?R-squared and seWhat Do You Think?Marginal and Partial SlopesPath DiagramWhat Do You Think?
Residual Plots
Inference for the Model: F-testWhat Do You Think?Inference for One CoefficientPrediction Intervals
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasEstimates of b0, b1 and b2Adjusted R2F-statisticStandard Deviation of ResidualsAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Which Explanatory Variables Belong in a Regression Model?
The Initial ModelIdentifying Other VariablesAdding Explanatory Variables
Variance Inflation FactorSigns of CollinearityWhat Do You Think?Remedies for Collinearity
Motivation State the QuestionMethod Describe the Data and Select An ApproachMechanics Do the AnalysisMessage Summarize the ResultsMotivation State the QuestionMethod Describe the Data and Select An ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasStandard Error of a Slope in Multiple RegressionVariance Inflation Factor (VIF)About the Data
Mix and MatchTrue/FalseThink About ItYou Do It
In 2001, Six Women Filed a Lawsuit Against Wal-Mart in Federal Court in San Francisco.
Confounding VariablesSubsets and ConfoundingWhat Do You Think?
Regression on SubsetsCombining RegressionsWhat Do You Think?Interpreting CoefficientsWhat Do You Think?
Checking for Similar Variances
Interactions and CollinearityParallel FitsWhat Do You Think?Motivation State the QuestionMethod Describe The Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
What Do You Think?
Key TermsObjectivesAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
At the Dawn of the 20th Century, More Than 10 Million Americans Toiled On Farms, More Than One-Third of the Domestic Workforce.
Comparing Groups in PlotsRelating the t-Test to RegressionWhat Do You Think?Comparing Several Groups Using RegressionInterpreting the EstimatesANOVA Regression ModelWhat Do You Think?
Checking ConditionsWhat Do You Think?F-Test for the Difference among MeansUnderstanding the F-TestConfidence Intervals
Tukey Confidence IntervalsBonferroni Confidence IntervalsWhat Do You Think?Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasNotation for DataFitted Values and ResidualsStandard Error for the Difference Between Two MeansTukey Percentiles q.025,n,JAbout the Data
Mix and MatchTrue/FalseThink About ItYou Do It
The Value of Goods Shipped Measures the Health of a Business.
SmoothingExponential SmoothingWhat Do You Think?
Polynomial TrendsMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsAutoregressionForecasting an AutoregressionWhat Do You Think?
Motivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the ResultsMotivation State the QuestionMethod Describe the Data and Select an ApproachMechanics Do the AnalysisMessage Summarize the Results
Key TermsObjectivesFormulasDurbin-Watson Statistic and AutocorrelationExponential Smoothing, Exponentially Weighted Moving Average (EWMA)About the Data
Mix and MatchTrue/FalseThink About ItYou Do It
Balanced ExperimentPreliminary Data Analysis
ModelPlan for AnalysisChecking the ModelTesting the FactorsRegression CoefficientsInteractions and One-way Anova
Data for ModelingPreliminary Analysis: Outliers and Collinearity
Avoiding Over-fittingRunning Stepwise RegressionInterpreting the Stepwise Model
Chapter 2
Mix and MatchTrue/FalseThink About ItYou Do It
Photo CreditsFront MatterChapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14Chapter 15Chapter 16Chapter 17Chapter 18Chapter 19Chapter 20Chapter 21Chapter 22Chapter 23Chapter 24Chapter 25Chapter 26Chapter 27Text CreditsChapter 5Chapter 9Back Matter

Content preview from Statistics for Business: Decision Making and Analysis, 3rd Edition

11.3 Properties of Binomial Random Variables

Mean and Variance

Because a binomial random variable is a sum of iid random variables, we can use the rules for expected values and variances from Chapter 10 to find its mean and variance. To find the mean of Y, the Addition Rule for Expected Values (the average of a sum is the sum of the averages) tells us that

\begin{matrix} E (Y) & = E (B_{1}) + E (B_{2}) + \dots + E (B_{n}) \\ = p + p + \dots + p \\ = n p \end{matrix}

The mean of a binomial random variable is the number of trials times the probability of success. We expect a fraction p of the trials to result in a success.

For the variance, use the Addition Rule for Variances. Because Bernoulli random variables are independent of one another, the variance of a binomial random variable is the sum of the variances.