What s in the Bag Lecture 4 Sections 1 4 1 1 4 2 Robb T Koether Hampden Sydney College Tue Jan 23 2012 Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 1 38 Outline 1 Bag A and Bag B 2 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 3 vs 4 Assignment Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 2 38 Review Quiz Example Review Quiz 1 The results of a study were found not to be statistically significant We may conclude that a b c d The null hypothesis was accepted The null hypothesis was not accepted The alternative hypothesis was accepted We cannot tell which was accepted Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 3 38 Review Quiz Example Review Quiz 2 The results of a study were found not to be statistically significant We may conclude that a b c d A Type I error could have been made A Type II error could have been made Either type of error could have been made Neither type of error could have been made Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 4 38 Review Quiz Answers Example Review Quiz Answers 1 a The null hypothesis was accepted 2 b A Type II error could have been made Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 5 38 Outline 1 Bag A and Bag B 2 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 3 vs 4 Assignment Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 6 38 Two Bags Two bags contain vouchers worth various dollar amounts Bag A 10 20 30 40 50 60 10 20 30 40 50 60 Bag B Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 7 38 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to cash in the vouchers in whichever bag you want Which bag should you choose Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 8 38 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to cash in the vouchers in whichever bag you want Which bag should you choose Oh one more thing Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 8 38 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to cash in the vouchers in whichever bag you want Which bag should you choose Oh one more thing You are handed one of the bags but you do not know which bag is it Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 8 38 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to cash in the vouchers in whichever bag you want Which bag should you choose Oh one more thing You are handed one of the bags but you do not know which bag is it You may look at one voucher in that bag Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 8 38 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to cash in the vouchers in whichever bag you want Which bag should you choose Oh one more thing You are handed one of the bags but you do not know which bag is it You may look at one voucher in that bag Based on that alone you must choose which bag to cash in Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 8 38 The Hypotheses The hypotheses are H0 You are holding Bag A H1 You are holding Bag B You will choose one voucher at random from the bag and read its value From that information you will decide which bag you believe you are holding Then you will choose the one that you believe is Bag B take the money and run Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 9 38 Decisions and Their Consequences The State of Nature It is Bag A It is Bag B It is Bag A switch bags Win 930 Win 470 It is Bag B keep the bag Win 470 Win 930 Our Decision Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 10 38 Outline 1 Bag A and Bag B 2 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 3 vs 4 Assignment Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 11 38 Decision Rules There are several possible decision rules some better than others We will look at three of them Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 12 38 Outline 1 Bag A and Bag B 2 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 3 vs 4 Assignment Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 13 38 A Decision Rule Decision Rule 1 Reject H0 if the voucher is worth 60 What is What is 10 20 30 40 50 60 10 Bag A Robb T Koether Hampden Sydney College 20 30 40 50 60 Bag B What s in the Bag Tue Jan 23 2012 14 38 Rejection and Acceptance Regions Definition Rejection Region The rejection region is the set of possible observed values that will lead to rejection of the null hypothesis Definition Acceptance Region The acceptance region is the set of possible observed values that will lead to acceptance of the null hypothesis Definition Critical Value s The critical value s is the value that separates the the two regions The critical value itself will be included in the rejection region Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 15 38 Decision Rule 1 10 20 30 40 50 60 Critical value Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 16 38 Decision Rule 1 Rejection region 10 20 30 40 50 60 Critical value Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 17 38 Decision Rule 1 Acceptance region 10 20 30 40 50 Rejection region 60 Critical value Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 23 2012 18 38 Compute Bag A 10 20 30 40 50 60 10 20 30 40 …
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