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# 3 Weekly Notes ECO 211

ECONOMIC PRINCIPLES AND PROBLEMS
Isaac Petit-Frere

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COURSE
ECONOMIC PRINCIPLES AND PROBLEMS
PROF.
Isaac Petit-Frere
TYPE
Bundle
PAGES
5
WORDS
KARMA
75 ?

1 review
ec

## Popular in Economcs

This 5 page Bundle was uploaded by an elite notetaker on Thursday August 27, 2015. The Bundle belongs to ECO 211 at University of Miami taught by Isaac Petit-Frere in Summer 2015. Since its upload, it has received 50 views. For similar materials see ECONOMIC PRINCIPLES AND PROBLEMS in Economcs at University of Miami.

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Date Created: 08/27/15
p1 p2 p3 4 a H0 Ha Not all population proportions are equal b Observed Frequencies fij Component A B C Total Defective 15 20 40 75 Good 485 480 460 1425 Total 500 500 500 1500 Expected Frequencies eij Component A B C Total Defective 25 25 25 75 Good 475 475 475 1425 Total 500 500 500 1500 Chi Square Calculations fij eij2 eij Component A B C Total Defective 400 100 900 1400 Good 21 05 47 M 12 1474 Degrees of freedom k 1 3 1 2 2 2 Z 6 Using the table with df 2 1474 shows the p value is less than 01 2 6 Using Excel or Minitab the p value corresponding to 1474 is 0006 p value g 05 reject H0 Conclude that the three suppliers do not provide equal proportions of defective components p1550003 D2 2050004 0 3 4050008 Multiple comparisons For Supplier A vs Supplier B 2635 dfk 13 1z 5991 71 13 170 17 031 03 041 04 CV 2 1 4 I J J 5991 0284 391 13 n n 500 500 l 1 Critical Significant Comparison pi 91 Difference mi 721 Value Diff gt CV A vs B 03 04 01 500 500 0284 A vs C 03 08 05 500 500 0351 Yes B vs C 04 08 04 500 500 0366 Yes Supplier A and supplier B are both significantly different from supplier C Supplier C can be eliminated on the basis of a significantly higher proportion of defective components Since suppliers A and supplier B are not significantly different in terms of the proportion defective components both of these suppliers should remain candidates for use by Benson p1p2 p3 p4 H0 Ha Not all population proportions are equal Observed Frequencies fij Social Net Great Britain Israel Russia USA Total Yes 344 265 301 500 1410 No 456 235 399 500 1590 800 500 700 1000 3000 Expected Frequencies eij Social Net Great Britain Israel Russia USA Total Yes 376 235 329 470 1410 No 424 265 371 530 1590 800 500 700 1000 3000 Chi Square Calculations fij eij2 eij Social Net Great Britain Israel Russia USA Total Yes 272 383 238 191 1085 No 242 340 211 170 962 952 2047 Degrees of freedom df k 1 4 1 3 252 252 Using the table with df 3 2047 shows the p Value is less than 01 2 6 Using Excel or Minitab the p Value corresponding to 2047 is 0001 S p Value 05 reject H0 Conclude the population proportions are not all equal Great Britain 344800 43 Israel 265500 53 Largest with 53 of adults Russia 301700 43 United States 5001000 50 Multiple pairwise comparisons 1 C lij39 Zin a p p p I ll n 2 7605 wheredfk 14 13and 7815 Comparison pi pj Difference n 72 CV Diff gt CVij GB VS I 043 053 010 800 500 00793 Yes GB V R 043 043 000 800 700 00716 GB VS USA 043 050 007 800 1000 00659 Yes IVS R 053 043 010 500 700 00814 Yes IVS USA 053 050 003 500 1000 00765 R VS USA 043 050 007 700 1000 00685 YeS Only two comparisons are not signi cant Great Britain and Russia and then Israel and United States All other comparisons show a significant difference H0 pABC 29pCBs 28pNBC 25p1ND Ha The proportions are not pABC 29 pCBs 28 pNBC 25 pm 18 Expected frequencies 30029 87 30028 84 30025 75 30018 54 61 87 62 84 63 75 64 Observed frequencies f1 95 f2 70 f3 89 f4 46 11 2 2 2 2 1295 87 70 84 89 75 46 54 87 84 75 54 687 k 1 3 degrees of freedom 252 252 Using the table with df 3 687 shows the p Value is between 05 and 10 2 26 Using Excel or Minitab the p Value corresponding to 687 is 0762 p Value gt 05 do not reject H0 There has not been a significant change in the Viewing audience proportions H0 Type of ticket purchased is independent of the type of ight Ha Type of ticket purchased is not independent of the type of ight Expected Frequencies 611 612 621 15073 622 6527 631 45568 632 19732 Observed Expected Frequency Frequency Chi square Ticket Flight fi ei fi ei2 ei First Domestic 29 35 59 122 First International 22 1541 282 Business Domestic 95 15073 2061 Business International 121 65 27 4759 Full Fare Domestic 518 455 68 852 Full Fare International 19732 1968 Totals 920 12 10043 Degrees of freedom r 1c 1 3 12 1 2 2 2 Z 26 Using the table with df 2 10043 shows the p Value is less than 005 2 26 Using Excel or Minitab the p Value corresponding to 10043 is 0000 lt p Value 05 reject H0 Conclude that the type of ticket purchased is not independent of the type of ight We can eXpect the type of ticket purchased to depend upon Whether the ight is domestic or international Column Percentages Type of Flight Type of Ticket Domestic International First Class 45 79 Business Class 148 435 Economy Class 807 486 A higher percentage of first class and business class tickets are purchased for international ights compared to domestic ights Economy class tickets are purchased more for domestic ights The first class or business class tickets are purchased for more than 50 of the international ights 79 435 514

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