Hypothesis Tests

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1、One-SampleHypothesisTestsHo:NullHypothesis–BenchmarkH1:AlternativeHypothesis–ThehypothesisbeingtestedTypeIErrorαP(RejectH0

2、H0isTrue)FalsePositiveTypeIIErrorβP(FailtoRejectH0

3、H0isFalse)FalseNegativePower1-βP(RejectH0

4、H0isFalse)SensitivityForagiventypeoftestandsample

5、size,thereisatradeoffbetweenαandβ.Theonlywaytoreducethembothsimultaneouslyistoincreasethesamplesize.Left-TailedTestTwo-TailedTestRight-TailedTest?0:?≥?0?0:?=?0?0:?≤?0?1:??0TheCriticalValueistheboundarybetweentheRejectandDoNotRejectregions.Itisthestan

6、dardizedscoreassociatedwithα.TheTestStatisticisthestandardizedscoreofthesamplestatisticbeingtested(inourcase,either?̅???).IftheTestStatisticismoreextremethantheCriticalValue,thereissufficientevidencetorejecttheH0.Thep-valueistheprobabilityassociatedwiththeTestStati

7、stic.Whenthep-valueis

8、?0ProbabilityUnknown?2??????=?associatedwitht-????−??????????2√?score.Cannotlookituponstatisticald.f.=n-1table.Testinga?????−???????????−?0Probability?????=Proportion?????−??????????√?0(1−?0)associatedwithZ-2?score.Lookituponstatisticaltable.Whentestingaproportion,

9、youmustfirstchecktodetermineifyoumayassumenormalityofthedistribution.Youmayassumenormalitywhen??≥10AND?(1−?)≥10.Two-SampleHypothesisTestsComparingTwoMeans-IndependentSamplesLeft-TailedTestTwo-TailedTestRight-TailedTest?0:?1−?2≥?0?0:?1−?2=?0?0:?1−?2≤?0?1:?1−?2

10、?1−?2≠?0?1:?1−?2>?0Case–TwoMeansCriticalValueTestStatisticP-Value1.Known?2?????−??????????(?̅̅1̅−?̅̅2̅)−(?1−?2)Probability?????−???????????????=associated2?2?2withZ-√1+2?1?2score.Lookituponstatisticaltable.2.Unknown?2-?????−??????????(?̅1−?̅2)−(?1−?2)ProbabilityAss

11、umedEqual?????−???????????????=associated2??2??2witht-√+?1?2score.?.?.=?1+?2−2Cannot(?1−1)?12+(?2−1)?22lookitup?2=on??1+?2−2statisticaltable.3.Un