Bag A and Bag BPossible Decision RulesDecision Rule #1Decision Rule #2Decision Rule #3 vs. AssignmentWhat’s in the Bag?Lecture 4Sections 1.4.1-1.4.2Robb T. KoetherHampden-Sydney CollegeTue, Jan 23, 2012Robb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 1 / 38Outline1Bag A and Bag B2Possible Decision RulesDecision Rule #1Decision Rule #2Decision Rule #33α vs. β4AssignmentRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 2 / 38Review QuizExample (Review Quiz)1The results of a study were found not to be statistically significant.We may conclude that(a) The null hypothesis was accepted.(b) The null hypothesis was not accepted.(c) The alternative hypothesis was accepted.(d) We cannot tell which was accepted.Robb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 3 / 38Review QuizExample (Review Quiz)2The results of a study were found not to be statistically significant.We may conclude that(a) A Type I error could have been made.(b) A Type II error could have been made.(c) Either type of error could have been made.(d) Neither type of error could have been made.Robb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 4 / 38Review Quiz AnswersExample (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 / 38Outline1Bag A and Bag B2Possible Decision RulesDecision Rule #1Decision Rule #2Decision Rule #33α vs. β4AssignmentRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 6 / 38Two BagsTwo bags contain vouchers worth various dollar amounts.10 605040302010 6050403020Bag ABag BRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 7 / 38Two BagsThe 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 isit.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 / 38Two BagsThe 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 isit.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 / 38Two BagsThe 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 isit.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 / 38Two BagsThe 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 isit.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 / 38Two BagsThe 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 isit.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 / 38The HypothesesThe 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 itsvalue.From that information, you will decide which bag you believe youare holding.Then you will choose the one that you believe is Bag B, take themoney and run.Robb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 9 / 38Decisions and Their ConsequencesIt is Bag A It is Bag BIt is Bag A(switch bags)It is Bag B(keep the bag)The State of NatureOur DecisionWin $930Win $930Win $470Win $470Robb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 10 / 38Outline1Bag A and Bag B2Possible Decision RulesDecision Rule #1Decision Rule #2Decision Rule #33α vs. β4AssignmentRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 11 / 38Decision RulesThere are several possible decision rules, some better thanothers.We will look at three of them.Robb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 12 / 38Outline1Bag A and Bag B2Possible Decision RulesDecision Rule #1Decision Rule #2Decision Rule #33α vs. β4AssignmentRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 13 / 38A Decision RuleDecision Rule #1Reject H0if the voucher is worth $60.What is α?What is β?10 605040302010 6050403020Bag A Bag BRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 14 / 38Rejection and Acceptance RegionsDefinition (Rejection Region)The rejection region is the set of possible observed values that willlead to rejection of the null hypothesis.Definition (Acceptance Region)The acceptance region is the set of possible observed values that willlead 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 / 38Decision Rule #110 6050403020Critical valueRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 16 / 38Decision Rule #110 6050403020Critical valueRejection regionRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue, Jan 23, 2012 17 / 38Decision Rule #110 6050403020Critical valueRejection regionAcceptance regionRobb T. Koether (Hampden-Sydney College) What’s in the Bag? Tue,
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