What s in the Bag Lecture 4 Sections 1 4 1 1 4 2 Robb T Koether Hampden Sydney College Tue Jan 19 2010 Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 1 41 Outline 1 Homework Review 2 Bag A and Bag B 3 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 4 Assignment 5 Answers to Even Numbered Problems Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 2 41 Outline 1 Homework Review 2 Bag A and Bag B 3 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 4 Assignment 5 Answers to Even Numbered Problems Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 3 41 Homework Review Exercise 1 11 p 67 A consumer protection agency received many complaints that the sodium content in a six ounce can of Star Kist tuna is greater then the 250 mg that is stated on the label of each can In response to these complaints the protection agency tested the following hypotheses H0 The average sodium content of all six ounce cans is 250 mg H1 The average sodium content of all six ounce cans is greater than 250 mg The data from the study were not statistically significant Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 4 41 Homework Review Exercise 1 7 p 68 a What hypothesis was supported Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 5 41 Homework Review Exercise 1 7 p 68 a What hypothesis was supported The null hypothesis was supported Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 5 41 Homework Review Exercise 1 7 p 68 a What hypothesis was supported The null hypothesis was supported b Was a complaint registered with the provider the Star Kist Co Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 5 41 Homework Review Exercise 1 7 p 68 a What hypothesis was supported The null hypothesis was supported b Was a complaint registered with the provider the Star Kist Co No Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 5 41 Homework Review Exercise 1 7 p 68 a What hypothesis was supported The null hypothesis was supported b Was a complaint registered with the provider the Star Kist Co No c Could a mistake have been made If so describe the mistake Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 5 41 Homework Review Exercise 1 7 p 68 a What hypothesis was supported The null hypothesis was supported b Was a complaint registered with the provider the Star Kist Co No c Could a mistake have been made If so describe the mistake Yes a Type II error could have been made A Type II error would be to conclude that the average sodium content of all six ounce cans is greater than 250 mg when in fact it is equal to 250 mg Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 5 41 Outline 1 Homework Review 2 Bag A and Bag B 3 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 4 Assignment 5 Answers to Even Numbered Problems Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 6 41 Two Bags Two bags contain vouchers with various dollar values 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 19 2010 7 41 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to choose whichever bag you want cash in the vouchers and keep the money Which bag should you choose Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 8 41 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to choose whichever bag you want cash in the vouchers and keep the money Which bag should you choose Oh one more thing Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 8 41 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to choose whichever bag you want cash in the vouchers and keep the money Which bag should you choose Oh one more thing The bags are indistinguishable from the outside and you are not allowed to look inside Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 8 41 Two Bags The vouchers in Bag A are worth 470 The vouchers in Bag B are worth 930 You get to choose whichever bag you want cash in the vouchers and keep the money Which bag should you choose Oh one more thing The bags are indistinguishable from the outside and you are not allowed to look inside However you may reach inside choose one voucher and read its value Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 8 41 The Hypotheses We are shown one of the bags The hypotheses are I I H0 The bag shown is Bag A H1 The bag shown is Bag B We will choose one voucher at random from the shown bag and read its value From that information we will decide which bag we believe we are holding Then we will choose the one that we believe is Bag B take the money and run Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 9 41 Decisions and Their Consequences We decide it is Bag A We decide it is Bag B Robb T Koether Hampden Sydney College It is Bag A Win 930 Win 470 What s in the Bag It is Bag B Win 470 Win 930 Tue Jan 19 2010 10 41 Outline 1 Homework Review 2 Bag A and Bag B 3 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 4 Assignment 5 Answers to Even Numbered Problems Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 11 41 Outline 1 Homework Review 2 Bag A and Bag B 3 Possible Decision Rules Decision Rule 1 Decision Rule 2 Decision Rule 3 4 Assignment 5 Answers to Even Numbered Problems Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 12 41 A Decision Rule Decision Rule 1 Reject H0 if the voucher is worth 60 What is What is Robb T Koether Hampden Sydney College What s in the Bag Tue Jan 19 2010 13 41 Rejection …
View Full Document
Unlocking...