Lecture 5.pptx - Introduction to Statistics Hypothesis...

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Introduction to Statistics
Hypothesis Testing
Hypothesis TestingWe are often interested in testing the validity of somestatementSuppose you want to determine whether the mean level ofa driver’s blood alcohol exceeds the legal limit after twodrinks….? Is the underlying mean return on this mutualfund different from the underlying mean return on itsbenchmark?You are interested in making aninferenceabout how thevalue of a parameter relates to a specific numerical value
Hypothesis TestingHypothesis testing: part of the branch of statistics known asstatistical inferenceA hypothesis is a statement about one or more populationsHypothesis testing allows us to use asampleto decidebetweentwo statementsmade about apopulationcharacteristic.These two statements are called theNull Hypothesisand theAlternative Hypothesis.
Terms Introduce in Prior ChapterPopulationall possible valuesSamplea portion of the populationStatistical inferencegeneralizing from a sample toa population with calculated degree of certaintyTwo forms of statistical inferenceHypothesis testingEstimationParametera characteristic of population, e.g., populationmean µStatisticcalculated from data in the sample, e.g., samplemean ()x
Review: Distinctions BetweenParameters and StatisticsParametersStatisticsSourcePopulationSampleNotationGreek (e.g., μ)Roman (e.g., )VaryNoYesCalculatedNoYesParametersStatisticsSourcePopulationSampleNotationGreek (e.g., μ)VaryNoYesCalculatedNoYes
The Elements of a Test ofHypothesisThe null hypothesisH0: The Null HypothesisThis is the hypothesis being tested. It is the statementthat we are attempting to disprove.“Portfolio returns are 5%”“My portfolio is no riskier than the market”
The Elements of a Test ofHypothesisThe Alternative HypothesisHA: The Alternative HypothesisThis is the hypothesis or claim which weinitially assume tobe falsebut which we may decidenot to reject if there issufficient evidence.If we disprove H0,we can accept the alternative hypothesis.
The Legal AnalogyThis procedure is familiar to us already from the legalsystem “Innocent until proven guilty”.The null hypothesis (not guilty) is only rejected infavour of the alternative (guilty) if thereis sufficientevidenceof this “beyond reasonable doubt”The null hypothesis will not be rejected unless the dataprovideconvincing evidencethat it is false.The alternative hypothesis is that which will beaccepted only if the data provide convincingevidenceof its truth
The HypothesesNull HypothesisH0: ‘There isno differencebetween the average number of streams per squarekilometer and the bedrock type.‘This is thehypothesis to be testedAlternative HypothesisHAorH1: ‘Thereis adifferencebetween the average number ofstreams per square kilometer and the bedrocktype.'
Steps in Hypothesis Testing1.Stating the hypotheses2.Identify the appropriate test statistic and it’sprobability distribution3.Specifying the significance level4.Stating the decision rule5.Collecting the data and calculating the test statistic6.Making the statistical decision
Formulating the Hypotheses

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Term
Spring
Professor
Myra O'Regan
Tags
Normal Distribution, Null hypothesis, Hypothesis testing, Statistical hypothesis testing, Type I and type II errors

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