What s in the Bag Lecture 3 Section 1 4 1 1 4 2 Tue Jan 18 2005 Two Bags Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B The Hypotheses H0 The shown bag is Bag A H1 The shown bag is Bag B Decisions and Errors H0 true H0 false Accept H0 Win 1890 Lose 560 Reject H0 Lose 560 Win 1890 Decision Rules Decision Rule A formal rule that tells us when to reject the null hypothesis Possible Decision Rules Decision Rule 0 Reject H0 if the voucher is worth 1000 What is What is Possible Decision Rules Decision Rule 1 Reject H0 if the voucher is worth either 60 or 1000 i e 60 Rejection and Accepance Regions Rejection Region The set of values for which we would reject H0 Acceptance Region The set of values for which we would accept H0 Critical Value The value that separates the rejection region from the acceptance region Decision Rule 1 60 Decision Rule 1 Rejection Region 60 Decision Rule 1 Acceptance Region Rejection Region 60 Decision Rule 1 Acceptance Region Rejection Region 60 Critical Value Compute Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B Compute Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B Compute Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B Compute 1 20 0 05 Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B Compute Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B Compute Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B Compute Bag A 1000 10 20 30 40 50 60 1000 1000 10 20 30 40 50 60 1000 Bag B Compute Bag A 1000 Bag B 10 20 30 40 50 60 1000 12 20 0 60 1000 10 20 30 40 50 60 1000 Most Extreme Value Direction of Extreme The direction in which are found the values that are least likely under H0 but at the same time are very likely under H1 Most Extreme Value The value that is least likely under H0 but is very likely under H1 Another Decision Rule Decision Rule 2 Reject H0 if the voucher is worth 50 vs If we decrease we will increase and If we decrease we will increase Is it possible to decrease both and at the same time Let s Do It Example 1 5 p 21 One Sided Rejection Region to the Left Let s do it 1 6 p 23 Enlarging the Rejection Region Example 1 6 p 24 Two Sided Rejection Region to the Left and to the Right
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