book

Statistics, 3E

by Robert A. Donnelly, Fatma Abdel-Raouf

July 2016

Intermediate to advanced

336 pages

8h 58m

English

Alpha

Read now

Unlock full access

What Is Statistics and Why Do You Need It?Types of StatisticsDescriptive Statistics–the Minor LeagueInferential Statistics–the Major LeaguePopulation vs. SampleParameter vs. StatisticEthics and Statistics–It’s a Dangerous World Out TherePractice Problems
The Importance of DataThe Sources of Data–Where Does All This Stuff Come From?Direct Observation–I’ll Be Watching YouExperiments–Who’s in Control?Surveys–Is That Your Final Answer?Data and Types of VariablesQuantitative vs. Qualitative VariablesDiscrete vs. Continuous VariablesDependent vs. Independent VariablesTypes of Measurement Scales–a Weighty TopicNominal Level of MeasurementOrdinal Level of MeasurementInterval Level of MeasurementRatio Level of MeasurementComputers to the RescueThe Role of Computers in StatisticsInstalling the Data Analysis Add-InPractice Problems
Frequency DistributionsThe Frequency Distribution(A Distant) Relative Frequency DistributionThe Cumulative Frequency DistributionThe Contingency TableCharting Your Course: GraphsHistogramLetting Excel Do Our Dirty WorkBar ChartPie ChartLine ChartThe Stem and Leaf Display–Statistical Flower PowerPractice Problems
Measures of Central TendencyMeanMedianModeWeighted MeanMeasures of Central Tendency for Grouped Data:How Does One Choose?Using Excel to Calculate Central TendencyPractice Problems

Measures of Dispersion for Ungrouped DataRangeVarianceUsing the Raw Score Method (When Grilling)Variance of a PopulationStandard DeviationMeasures of Dispersion for Grouped DataMeasures of Relative PositionQuartilesInterquartile Range (IQR)Excel to the RescuePractice Problems
What is Probability?Classical ProbabilityEmpirical ProbabilitySubjective ProbabilityRelationship Between EventsMutually Exclusive EventsIndependent EventsComplementary EventsUnion and Intersection of EventsThe Union of Events: A Marriage Made in HeavenThe Intersection of EventsPractice Problems
Addition Rule of ProbabilitiesConditional ProbabilityMultiplication Rule of ProbabilitiesBayes’ TheoremCounting PrinciplesThe Fundamental Counting RulePermutationsCombinationsUsing Excel to Calculate Factorials, Permutations, and CombinationsPractice Problems
Basic Concepts of Probability DistributionsRandom VariablesProbability DistributionsRules for Discrete Probability DistributionsThe Mean of Discrete Probability DistributionsThe Variance and Standard Deviation of Discrete Probability DistributionsPractice Problems
Characteristics of a Binomial ExperimentThe Binomial Probability DistributionBinomial Probability TablesUsing Excel to Calculate Binomial ProbabilitiesThe Mean and Standard Deviation for the Binomial DistributionPractice Problems
Characteristics of a Poisson ProcessThe Poisson Probability DistributionPoisson Probability TablesUsing Excel to Calculate Poisson ProbabilitiesUsing the Poisson Distribution as an Approximation to the Binomial DistributionPractice Problems
Characteristics of the Normal Probability DistributionCalculating Probabilities for the Normal DistributionCalculating Probability Using the Z-ScoreUsing the Standard Normal TableThe Area Under the Normal Distribution and the Empirical RuleCalculating Normal Probabilities Using ExcelUsing the Normal Distribution as an Approximation to the Binomial DistributionPractice Problems
Why Sample?Random SamplingSimple Random SamplingSystematic SamplingCluster SamplingStratified SamplingSampling Error and Sampling BiasSampling ErrorSampling BiasExamples of Poor Sampling TechniquesPractice Problems
What Is a Sampling Distribution?Sampling Distribution of the Sample MeansMean of the Sampling Distribution of the Sample MeansStandard Error of the Sampling Distribution of the Sample MeansThe Central Limit TheoremPutting the Central Limit Theorem to WorkSampling Distribution of the ProportionCalculating the Sample ProportionCalculating the Standard Error of the ProportionPractice Problems
The Basics of Confidence IntervalsPoint Estimate and Interval EstimateThe Principle of Confidence IntervalsThe Probability of an Error (the Alpha Value)Confidence Intervals for the Population MeanWhen the Population Standard Deviation Is KnownBeware of Interpretation of the Confidence Interval!The Effect of Changing Confidence LevelsThe Effect of Changing the Sample SizeWhen the Population Standard Deviation Is UnknownWhen the Population Standard Deviation Is Unknown and with Small SamplesDetermining Sample Size for the Population MeanUsing Excel’s CONFIDENCE FunctionConfidence Intervals for the Population Proportion with Large SamplesCalculating the Confidence Interval for the Population ProportionDetermining Sample Size for the ProportionPractice Problems
Hypothesis Testing: The Traditional MethodProcedures for Hypothesis Testing1. The Null and Alternative Hypotheses2. The Level of Significance3. The Test Statistic4. The Critical Value5. State Your DecisionOne-Tail vs. Two-Tail TestsTwo-Tail Hypothesis TestingOne-Tail Hypothesis TestingHypothesis Testing for the Population MeanWhen Sigma Is KnownWhen Sigma Is Unknown and Using a Large SampleWhen Sigma Is Unknown and Using a Small SampleThe Role of Alpha in Hypothesis TestingThe p-Value MethodThe p-Value for a One-Tail TestThe p-Value for a Two-Tail TestUsing Excel for Hypothesis TestingUsing Excel’s NORM.S.DIST FunctionUsing Excel’s T.DIST, T.DIST.RT, and T.DIST.2T FunctionsUsing Excel’s T.INV and T.INV.2T FunctionsHypothesis Testing for the Population Proportion with Large SamplesOne-Tail Hypothesis Test for the ProportionTwo-Tail Hypothesis Test for the ProportionPractice Problems
The Concept of Testing Two PopulationsSampling Distribution for the Difference in MeansTesting for the Differences Between Two Population Means with Independent SamplesWhen the Population Standard Deviations Are KnownTesting a Difference Other Than ZeroWhen the Population Standard Deviations Are UnknownUnequal Population Variances When the Population Standard Deviations Are UnknownEqual Population Variances When the Population Standard Deviations Are UnknownTo Pool or Not to Pool?Testing for Differences Between Means with Dependent SamplesLetting Excel Do the Grunt WorkTesting for Differences Between Proportions with Independent SamplesPractice Problems
A Solutions to “Practice Problems”

Content preview from Statistics, 3E

CHAPTER13

Sampling Distributions

In This Chapter

Using sampling distributions of the mean and proportion
Working with the central limit theorem
Using the standard error of the sampling mean and proportion

In Chapter 12, we praised the wonders of using samples in our statistical analysis because it was more efficient than measuring an entire population. In this chapter, we’ll discover another benefit of using samples–sampling distributions.

Sampling distributions describe how sample averages behave. You may be surprised to hear they behave very well–even better than the populations from which they are drawn. Good behavior means we can do a ...