What’s in the Bag?Two BagsThe HypothesesDecisions and ErrorsDecision RulesPossible Decision RulesSlide 7Rejection and Accepance RegionsDecision Rule #1Slide 10Slide 11Slide 12Compute Slide 14Slide 15Slide 16Compute Slide 18Slide 19Slide 20Most Extreme ValueAnother Decision Rule vs. Let’s Do It!What’s in the What’s in the Bag?Bag?Lecture 3Lecture 3Section 1.4.1 – 1.4.2Section 1.4.1 – 1.4.2Tue, Jan 18, 2005Tue, Jan 18, 2005Two BagsTwo Bags-1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag BThe HypothesesThe HypothesesHH00: The shown bag is Bag A.: The shown bag is Bag A.HH11: The shown bag is Bag B.: The shown bag is Bag B.Decisions and ErrorsDecisions and ErrorsWin $1890Win $1890Lose $560Lose $560H0 true H0 falseAccept H0Reject H0Decision RulesDecision RulesDecision RuleDecision Rule – A formal rule that – A formal rule that tells us when to reject the null tells us when to reject the null hypothesis.hypothesis.Possible Decision RulesPossible Decision RulesDecision Rule #0Decision Rule #0Reject Reject HH00 if the voucher is worth $1000. if the voucher is worth $1000.What is What is ??What is What is ??Possible Decision RulesPossible Decision RulesDecision Rule #1Decision Rule #1Reject Reject HH00 if the voucher is worth either if the voucher is worth either $60 or $1000, i.e., $60 or $1000, i.e., $60. $60.Rejection and Accepance Rejection and Accepance RegionsRegionsRejection RegionRejection Region – The set of values – The set of values for which we would reject for which we would reject HH00 . .Acceptance RegionAcceptance Region – The set of – The set of values for which we would accept values for which we would accept HH00 ..Critical ValueCritical Value – The value that – The value that separates the rejection region from separates the rejection region from the acceptance region.the acceptance region.Decision Rule #1Decision Rule #1$60Decision Rule #1Decision Rule #1$60Rejection RegionDecision Rule #1Decision Rule #1$60Rejection RegionAcceptance RegionDecision Rule #1Decision Rule #1$60Rejection RegionAcceptance RegionCritical ValueCompute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag BCompute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag BCompute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag BCompute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag B = 1/20 = 0.05Compute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag BCompute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag BCompute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag BCompute Compute -1000 10 20 30 40 60 100050Bag A-1000 10 20 30 40 60 100050Bag B = 12/20 = 0.60Most Extreme ValueMost Extreme ValueDirection of Extreme Direction of Extreme – The direction – The direction in which are found the values that in which are found the values that are least likely under are least likely under HH00 but at the but at the same time are very likely under same time are very likely under HH11..Most Extreme ValueMost Extreme Value – The value that – The value that is least likely under is least likely under HH00 but is very but is very likely under likely under HH11..Another Decision RuleAnother Decision RuleDecision Rule #2Decision Rule #2Reject Reject HH00 if the voucher is worth if the voucher is worth $50. $50. vs. vs. If we decrease If we decrease , we will increase , we will increase , , andandIf we decrease If we decrease , we will increase , we will increase ..Is it possible to decrease both Is it possible to decrease both and and at the same time? at the same time?Let’s Do It!Let’s Do It!Example 1.5, p. 21 – One-Sided Example 1.5, p. 21 – One-Sided Rejection Region to the Left.Rejection Region to the Left.Let’s do it! 1.6, p. 23 – Enlarging the Let’s do it! 1.6, p. 23 – Enlarging the Rejection Region.Rejection Region.Example 1.6, p. 24 – Two-Sided Example 1.6, p. 24 – Two-Sided Rejection Region to the Left and to Rejection Region to the Left and to the Right.the
View Full Document
Unlocking...