Math 533

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Team League (American 1, National 0) Built (Year Stadium Was Built) Size (Stadium Capacity) Salary (Total 2000 Team Salary $ Mil) Attendance (Total 2000 Team Attendance) Wins (Number of Wins in 2000) ERA (Earned Run Average) Batting (Team Batting Average) HR (Number of Home Runs for the Team) Surface (Natural 0, Artificial 1)

Stolen (Stolen Bases) Errors (Team Errors) Year Average (Average Player Salary) Median (Median Player Salary) x1 Team Boston New York Yankees Oakland Baltimore Anaheim Cleveland Chicago Toronto Minnesota Tampa Bay Texas Detroit Seattle Kansas City Atlanta Arizona Houston Cincinnati New York Mets Pittsburgh Los Angeles San Diego Montreal San Francisco St. Louis Florida Philadelphia Milwaukee Chicago Cubs Colorado x2 League 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x3

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Built 1912 1923 1966 1992 1966 1994 1991 1989 1982 1990 1994 2000 1999 1973 1993 1998 2000 1970 1964 1970 1962 1967 1976 1900 1966 1987 1971 1953 1914 1995 x4 Size 33,871 57,746 43,662 48,262 45,050 43,368 44,321 50,516 48,678 44,027 52,000 40,000 45,611 40,529 50,062 49,075 42,000 52,953 55,775 47,972 56,000 53,166 46,500 40,800 49,625 42,531 62,411 43,000 38,957 50,381 x5 Salary 93. 9 113. 4 33. 0 59. 2 58. 7 78. 7 36. 9 54. 6 15. 8 55. 2 61. 4 60. 6 62. 6 24. 5 95. 0 80. 8 52. 0 35. 1 89. 7 31. 9 94. 2 54. 7 28. 0 54. 2 72. 4 25. 9 36. 7 33. 8 51. 1 56. 0 x6

Attendance 2,585,895 3,227,657 1,728,885 3,297,031 2,066,982 3,456,278 1,947,799 1,819,919 1,059,415 1,479,782 2,800,075 2,533,753 3,148,317 1,677,915 3,234,304 2,819,539 3,056,139 2,577,371 2,820,530 1,748,908 3,011,539 2,423,149 926,272 3,318,800 3,336,493 1,218,326 1,612,769 1,573,621 2,789,511 3,295,129 x7 Wins 85 87 91 74 82 90 95 83 69 69 71 79 91 77 95 85 72 85 94 69 86 76 67 97 95 79 65 73 65 82 Tables and Data Sets 267 Appendix D Data Set 2 — Major League Baseball (continued) x1 Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 x7 Wins 5 87 91 74 82 90 95 83 69 69 71 79 91 77 95 85 72 85 94 69 86 76 67 97 95 79 65 73 65 82 x8 ERA 4. 23 4. 76 4. 58 5. 37 5. 00 4. 84 4. 66 5. 14 5. 14 4. 86 5. 52 4. 71 4. 49 5. 48 4. 05 4. 35 5. 42 4. 33 4. 16 4. 94 4. 10 4. 52 5. 13 4. 21 4. 38 4. 59 4. 77 4. 63 5. 25 5. 26 x9 Batting 0. 267 0. 277 0. 270 0. 272 0. 280 0. 288 0. 286 0. 275 0. 270 0. 257 0. 283 0. 275 0. 269 0. 288 0. 271 0. 265 0. 278 0. 274 0. 263 0. 267 0. 257 0. 254 0. 266 0. 278 0. 270 0. 262 0. 251 0. 246 0. 256 0. 294 x10 HR 167 205 239 184 236 221 216 244 116 162 173 177 198 150 179 179 249 200 198 168 211 157 178 226 235 160 144 177 183 161 11 Surface 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 x12 Stolen 318 182 184 208 202 218 158 198 128 228 130 110 164 236 198 204 222 162 266 202 212 212 246 194 138 208 154 172 188 204 x13 Errors 109 109 134 116 134 72 133 100 102 118 135 105 99 102 129 107 133 111 118 132 135 141 132 93 111 125 100 118 100 94 Team Boston New York Yankees Oakland Baltimore Anaheim Cleveland Chicago Toronto Minnesota Tampa Bay Texas Detroit Seattle Kansas City Atlanta Arizona Houston Cincinnati New York Mets Pittsburgh Los Angeles San Diego Montreal San Francisco St.

Louis Florida Philadelphia Milwaukee Chicago Cubs Colorado 268 Appendixes Appendix D Data Set 2 — Major League Baseball (concluded) x14 Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 x15 Average 52,300 74,000 97,800 121,900 146,500 196,500 245,000 289,000 325,900 368,998 410,517 402,579 430,688 489,539 589,483 845,383 1,012,424 1,062,780 1,154,486 1,094,440 1,101,455 1,314,420 1,384,530 1,567,873 1,983,849 16 Median * * * * * * * 207,500 229,750 265,833 275,000 235,000 235,000 280,000 350,000 412,000 392,500 371,500 450,000 275,000 300,000 400,000 427,500 495,000 700,000 Tables and Data Sets 269 Appendix E Data Set 3 — OECD x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x1 Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Luxembourg Mexico Netherlands New Zealand Norway Poland Portugal Spain Sweden Switzerland Turkey United Kingdom United States Country G7 Member (1 Yes, 0 No)

Total area of country in thousand square kilometers Population in thousands Percent of population over 65 years of age Exchange rate per U. S. dollar Gross Domestic Product at current exchange rate in billions of dollars Energy use in millions of tons of oil equivalent Index of total manufacturing (1900 Total labor force in thousands Region (1 x2 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 100) Far East, 2 x3 7,687 84 31 9,976 79 43 338 549 357 132 93 103 70 301 378 98 3 1,973 41 269 324 313 92 505 450 41 781 245 9,373 Europe, 3 x5 12. 1 15 16. 1 12. 2 13. 4 15. 1 14. 4 15. 15. 8 15. 8 14. 2 11. 4 11. 5 15. 8 14. 5 6. 1 14. 2 4. 8 13. 3 11. 6 15. 9 11. 3 14. 8 15. 6 17. 3 14. 9 4. 8 15. 7 12. 8 North America) x6 x7 390. 9 228. 7 268. 2 579. 2 56. 2 174. 9 125. 1 1,536. 6 235. 35 122. 4 44 7. 3 70. 7 1,243. 2 4,595. 2 484. 8 17 329. 4 396 65. 9 157. 8 134. 4 103. 6 584. 9 251. 7 294. 3 181. 5 1,153. 4 7,388. 1 x4 18,289 8,060 10,157 29,964 10,316 5,262 5,125 58,380 81,877 10,465 10,193 270 3,621 57,473 125,864 45,545 418 96,582 15,494 3,640 4,370 38,618 9,935 39,270 8,901 7,085 62,695 58,782 265,557 x8 100. 61 27. 19 56. 4 236. 17 40. 4 22. 87 31. 48 254. 349. 55 24. 39 25. 47 2. 27 11. 96 161. 14 510. 36 162. 87 3. 45 141. 38 75. 8 16. 3 23. 15 108. 41 19. 15 101. 41 52. 57 25. 62 65. 52 234. 72 2,134. 96 x9 109 111 108 112 117 121 98 97 98 x10 9,184 3,876 4,297 15,209 5,175 2,822 2,531 25,613 39,294 4,249 4,048 148 1,494 23,385 67,110 21,188 218 34,325 7,516 1,797 2,246 17,203 4,885 16,159 4,310 3,967 22,736 28,552 135,231 x11 1 2 2 3 2 2 2 2 2 2 2 2 2 2 1 1 2 3 2 1 2 2 2 2 2 2 2 2 3 1. 509 12. 51 36. 61 1. 426 34. 73 6. 771 5. 369 5. 955 1. 777 279. 6 201. 3 71. 71 0. 687 1743 129. 4 1477 8. 123 2. 004 1. 689 7. 25 3. 532 181. 5 150. 7. 785 1. 44 199,026 0. 603 1 175 104 98 163 100 118 109 119 115 97 103 121 103 129 102 118 270 Appendixes Appendix F Data Set 4 — Northwest Ohio School Districts x1 x2 x3 x4 x5 x6 x7 x8 x9 x1 Bluffton Shawnee Spencerville Delphos Elida Lima Northeastern Ayersville Defiance Hicksville Central Berlin-Milan Perkins Huron Margaretta Sandusky Kelleys Island Pettisville Wauseon Evergreen Archbold-Area Pike-Delta-York Gorham-Fayette Swanton Arlington Vanlue Liberty-Benton Van Buren Cory-Rawson Arcadia McComb Findlay Ada Kenton Liberty Center Patrick Henry Napoleon Area Holgate Monroeville

Name of district Number of students Mean family income in the district ($) Mean property value in the district ($) Percent of families receiving welfare Mean salary of classroom teachers ($) Amount spent per pupil ($) Mean daily attendance Percent passing 12th grade proficiency exam x2 1,132 2,472 1,026 1,104 3,204 5,963 1,194 921 3,046 990 1,216 1,593 2,038 1,494 1,560 4,426 20 503 1,864 1,238 1,401 1,559 487 1,725 685 346 954 840 794 597 805 5,758 855 2,228 1,009 1,176 2,331 605 686 x3 4,487 29,777 23,161 21,792 24,446 18,394 26,428 28,228 23,812 22,448 24,189 25,223 25,586 27,135 23,849 19,529 19,854 25,079 23,408 23,826 26,706 23,396 22,405 24,596 26,175 24,709 28,718 28,964 23,904 24,305 23,754 24,269 23,029 20,418 24,723 23,061 25,304 23,962 22,942 x4 62,678 130,910 51,645 88,453 65,550 44,138 88,789 82,707 56,333 56,411 53,923 76,878 117,545 105,588 74,601 72,425 802,081 53,948 60,896 69,432 107,547 48,638 57,221 69,320 55,478 49,606 77,503 151,992 69,242 78,102 69,347 92,648 52,655 61,155 57,685 63,134 84,245 49,709 63,103 5 1. 8 2. 6 5. 4 6. 2 8. 9 33. 8 1. 7 3. 9 11. 2 7 4. 6 4 3. 3 4. 6 2. 8 25. 2 11. 4 3. 9 4. 9 5. 2 4. 1 6. 1 6. 9 6. 3 2. 7 4. 1 1. 5 1. 8 2. 4 2. 5 5. 7 7. 6 5. 3 13. 8 4. 1 5. 2 6. 6 6 4. 3 x6 31,221 34,860 30,155 32,273 32,876 33,142 30,919 32,850 34,750 34,224 34,430 32,166 39,352 33,433 37,084 36,042 27,144 31,159 32,499 32,353 35,982 31,310 33,166 33,690 31,821 28,411 30,330 33,447 31,241 30,738 28,986 35,879 28,479 30,907 30,904 31,895 32,773 31,324 30,838 x7 ,130 2,570 2,262 2,506 2,250 2,657 2,431 2,693 2,438 2,351 2,496 2,564 2,861 2,968 2,464 2,766 11,226 2,834 2,252 2,250 2,837 2,309 2,492 2,615 2,205 2,420 2,063 2,584 2,416 2,752 2,321 2,860 2,380 2,512 2,431 2,552 2,422 2,454 2,474 x8 95. 7 94. 7 95. 5 96. 5 94. 1 92. 3 96. 1 95. 6 94. 2 95. 7 94. 8 96. 1 95. 8 95. 4 95. 5 93 95 96. 1 95. 3 95 96. 2 94. 8 94. 6 94. 9 96. 5 96. 2 96. 7 96. 4 96. 4 95. 9 95. 9 94. 9 95. 9 93. 7 95. 8 95. 9 94. 6 94. 9 95. 8 x9 85 73 68 65 62 40 72 68 63 59 56 77 74 74 66 37 100 78 75 72 69 66 51 50 84 83 78 75 73 64 61 60 69 54 82 75 73 71 64 Tables and Data Sets 271 Appendix F

Data Set 4 — Northwest Ohio School Districts (concluded) x1 Bellevue Willard Norwalk Ottawa Hills Anthony Wayne Sylvania Maumee Oregon Washington Springfield Toledo Benton Carroll Salem Danbury Genoa Port Clinton Put-in-Bay Paulding Ottoville Columbus Grove Kalida Continental Ottawa-Glandorf Pandora-Gilboa Leipsic Gibsonburg Lakota Fremont Woodmore Clyde–Green Springs Bettsville Seneca East Old Fort Hopewell-Loudon New Riegel Tiffin Fostoria Van Wert Edon-Northwest Milcreek–West Unity Bryan North Central Montpelier Edgerton Stryker Perrysburg Elmwood Bowling Green Otsego Northwood Eastwood Lake Rossford North Baltimore Upper Sandusky Carey 2 2,276 2,300 2,650 933 3,178 7,822 3,009 3,594 7,154 3,575 36,790 2,063 635 1,584 2,238 70 1,993 610 866 775 792 1,749 632 748 983 1,332 5,156 1,141 2,368 347 1,183 540 870 459 3,632 2,742 2,504 744 788 2,266 757 1,172 767 579 3,839 1,237 3,534 1,643 1,091 1,739 1,665 2,087 839 1,801 915 x3 4,025 23,304 21,551 45,723 29,215 32,114 27,604 24,525 23,507 26,048 21,079 23,899 21,325 25,321 20,941 19,266 22,677 24,128 23,562 24,456 23,625 25,363 23,806 20,941 23,312 22,678 22,327 26,460 23,854 22,103 22,656 23,208 22,103 23,314 21,246 20,809 22,728 23,035 21,302 22,607 21,871 20,787 22,429 24,084 32,773 22,179 21,307 24,614 25,905 25,043 23,559 25,360 22,075 21,063 21,658 x4 6,912 58,832 72,266 122,356 88,004 101,503 117,921 123,599 102,485 98,346 62,668 237,206 182,360 53,120 129,961 426,419 46,163 46,582 55,568 44,267 37,277 64,288 55,446 62,648 46,098 55,933 74,874 90,484 55,724 37,269 50,895 50,712 72,201 41,376 65,291 62,268 67,932 38,462 40,239 81,152 59,396 44,383 54,040 65,532 97,888 47,644 84,682 57,601 77,077 67,929 95,859 123,725 58,383 68,348 51,497 x5 6. 9 14. 3 12. 2 0. 2 3. 1 3. 8 3. 9 8. 7 11. 8 12. 2 42. 8 4. 7 3. 2 4. 8 10. 5 1. 4 8. 6 0. 2 8. 4 0. 7 10 6. 5 1. 2 16. 1 17. 8 10. 16. 2 10. 9 7 6. 1 4. 8 19. 3 4. 7 2. 7 9 20. 4 7. 1 2. 7 3. 2 4. 2 2. 9 8. 2 4. 1 3. 4 2. 6 7. 5 7. 5 5 7. 9 4. 7 6. 2 7. 2 10. 6 3. 9 6 x6 32,164 35,042 37,145 43,256 35,617 39,684 41,634 35,848 39,155 34,437 36,190 42,734 34,971 34,661 39,542 30,242 32,928 26,125 30,476 28,962 28,945 31,185 27,693 30,282 31,244 30,765 37,759 32,296 33,998 27,466 29,940 28,195 30,644 29,099 35,513 34,241 33,885 30,833 31,582 32,643 31,978 33,243 28,975 33,855 40,320 30,434 37,983 36,065 35,536 35,742 38,046 39,476 29,579 32,778 30,968 x7 ,374 2,347 2,384 4,150 2,844 2,943 3,933 2,941 2,997 2,774 2,611 3,444 3,158 2,845 2,926 7,824 2,560 2,588 2,174 2,274 2,225 2,154 2,078 2,811 2,242 2,306 2,616 2,227 2,383 2,394 2,435 2,743 2,564 2,501 2,506 2,455 2,511 1,916 2,382 2,706 2,349 2,654 2,470 2,617 3,011 2,643 2,849 2,539 2,979 2,499 2,820 3,258 2,331 2,267 2,513 x8 95. 1 94. 6 94 95. 7 95. 3 95. 5 95 94. 7 93. 7 93. 8 90. 7 95. 6 95. 3 95. 9 94. 5 94. 5 94. 5 99. 8 96. 2 96. 8 95. 5 96. 5 96. 5 93. 9 94. 4 95. 2 94. 7 96. 5 94. 6 95. 8 95. 9 96 94. 6 97 94. 7 92. 7 95. 3 95. 1 95. 9 95. 2 95. 6 94. 8 95. 9 95. 7 96. 1 95. 2 94. 7 95. 4 94. 9 95. 9 95. 2 94. 9 94. 5 95. 95. 5 x9 55 53 50 95 75 72 69 52 51 49 28 81 65 65 50 33 59 86 84 81 79 77 67 47 71 66 57 56 47 83 80 78 74 73 67 34 61 73 71 69 68 67 61 47 98 68 68 64 61 60 55 54 50 62 59 272 Appendixes Appendix G Critical Values of the F Distribution at a 5 Percent Level of Significance . 05 0 F Degrees of Freedom for the Numerator 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 60 120 161 18. 5 10. 1 7. 71 6. 61 5. 99 5. 59 5. 32 5. 12 4. 96 4. 84 4. 75 4. 67 4. 60 4. 54 4. 49 4. 45 4. 41 4. 38 4. 35 4. 32 4. 30 4. 28 4. 26 4. 24 4. 17 4. 08 4. 00 3. 92 3. 84 2 200 19. 0 9. 55 6. 94 5. 79 5. 14 4. 74 4. 46 4. 26 4. 0 3. 98 3. 89 3. 81 3. 74 3. 68 3. 63 3. 59 3. 55 3. 52 3. 49 3. 47 3. 44 3. 42 3. 40 3. 39 3. 32 3. 23 3. 15 3. 07 3. 00 3 216 19. 2 9. 28 6. 59 5. 41 4. 76 4. 35 4. 07 3. 86 3. 71 3. 59 3. 49 3. 41 3. 34 3. 29 3. 24 3. 20 3. 16 3. 13 3. 10 3. 07 3. 05 3. 03 3. 01 2. 99 2. 92 2. 84 2. 76 2. 68 2. 60 4 225 19. 2 9. 12 6. 39 5. 19 4. 53 4. 12 3. 84 3. 63 3. 48 3. 36 3. 26 3. 18 3. 11 3. 06 3. 01 2. 96 2. 93 2. 90 2. 87 2. 84 2. 82 2. 80 2. 78 2. 76 2. 69 2. 61 2. 53 2. 45 2. 37 5 230 19. 3 9. 01 6. 26 5. 05 4. 39 3. 97 3. 69 3. 48 3. 33 3. 20 3. 11 3. 03 2. 96 2. 90 2. 85 2. 81 2. 77 2. 74 2. 71 2. 68 2. 66 2. 64 2. 62 2. 60 2. 53 2. 5 2. 37 2. 29 2. 21 6 234 19. 3 8. 94 6. 16 4. 95 4. 28 3. 87 3. 58 3. 37 3. 22 3. 09 3. 00 2. 92 2. 85 2. 79 2. 74 2. 70 2. 66 2. 63 2. 60 2. 57 2. 55 2. 53 2. 51 2. 49 2. 42 2. 34 2. 25 2. 18 2. 10 7 237 19. 4 8. 89 6. 09 4. 88 4. 21 3. 79 3. 50 3. 29 3. 14 3. 01 2. 91 2. 83 2. 76 2. 71 2. 66 2. 61 2. 58 2. 54 2. 51 2. 49 2. 46 2. 44 2. 42 2. 40 2. 33 2. 25 2. 17 2. 09 2. 01 8 239 19. 4 8. 85 6. 04 4. 82 4. 15 3. 73 3. 44 3. 23 3. 07 2. 95 2. 85 2. 77 2. 70 2. 64 2. 59 2. 55 2. 51 2. 48 2. 45 2. 42 2. 40 2. 37 2. 36 2. 34 2. 27 2. 18 2. 10 2. 02 1. 94 9 241 19. 4 8. 81 6. 00 4. 77 4. 10 3. 68 3. 39 3. 18 3. 02 2. 90 2. 80 2. 71 2. 5 2. 59 2. 54 2. 49 2. 46 2. 42 2. 39 2. 37 2. 34 2. 32 2. 30 2. 28 2. 21 2. 12 2. 04 1. 96 1. 88 10 242 19. 4 8. 79 5. 96 4. 74 4. 06 3. 64 3. 35 3. 14 2. 98 2. 85 2. 75 2. 67 2. 60 2. 54 2. 49 2. 45 2. 41 2. 38 2. 35 2. 32 2. 30 2. 27 2. 25 2. 24 2. 16 2. 08 1. 99 1. 91 1. 83 12 244 19. 4 8. 74 5. 91 4. 68 4. 00 3. 57 3. 28 3. 07 2. 91 2. 79 2. 69 2. 60 2. 53 2. 48 2. 42 2. 38 2. 34 2. 31 2. 28 2. 25 2. 23 2. 20 2. 18 2. 16 2. 09 2. 00 1. 92 1. 83 1. 75 15 246 19. 4 8. 70 5. 86 4. 62 3. 94 3. 51 3. 22 3. 01 2. 85 2. 72 2. 62 2. 53 2. 46 2. 40 2. 35 2. 31 2. 27 2. 23 2. 20 2. 18 2. 15 2. 13 2. 11 2. 09 2. 01 1. 92 1. 84 1. 75 1. 7 20 248 19. 4 8. 66 5. 80 4. 56 3. 87 3. 44 3. 15 2. 94 2. 77 2. 65 2. 54 2. 46 2. 39 2. 33 2. 28 2. 23 2. 19 2. 16 2. 12 2. 10 2. 07 2. 05 2. 03 2. 01 1. 93 1. 84 1. 75 1. 66 1. 57 24 249 19. 5 8. 64 5. 77 4. 53 3. 84 3. 41 3. 12 2. 90 2. 74 2. 61 2. 51 2. 42 2. 35 2. 29 2. 24 2. 19 2. 15 2. 11 2. 08 2. 05 2. 03 2. 01 1. 98 1. 96 1. 89 1. 79 1. 70 1. 61 1. 52 30 250 19. 5 8. 62 5. 75 4. 50 3. 81 3. 38 3. 08 2. 86 2. 70 2. 57 2. 47 2. 38 2. 31 2. 25 2. 19 2. 15 2. 11 2. 07 2. 04 2. 01 1. 98 1. 96 1. 94 1. 92 1. 84 1. 74 1. 65 1. 55 1. 46 40 251 19. 5 8. 59 5. 72 4. 46 3. 77 3. 34 3. 04 2. 83 2. 66 2. 53 2. 43 2. 34 2. 27 2. 20 2. 5 2. 10 2. 06 2. 03 1. 99 1. 96 1. 94 1. 91 1. 89 1. 87 1. 79 1. 69 1. 59 1. 50 1. 39 Degrees of Freedom for the Denominator Tables and Data Sets 273 Appendix G Critical Values of the F Distribution at a 1 Percent Level of Significance . 01 0 F Degrees of Freedom for the Numerator 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 60 120 4052 98. 5 34. 1 21. 2 16. 3 13. 7 12. 2 11. 3 10. 6 10. 0 9. 65 9. 33 9. 07 8. 86 8. 68 8. 53 8. 40 8. 29 8. 18 8. 10 8. 02 7. 95 7. 88 7. 82 7. 77 7. 56 7. 31 7. 08 6. 85 6. 63 2 5000 99. 0 30. 8 18. 0 13. 3 10. 9 9. 55 8. 65 8. 02 7. 56 7. 21 6. 93 6. 70 6. 51 6. 36 6. 3 6. 11 6. 01 5. 93 5. 85 5. 78 5. 72 5. 66 5. 61 5. 57 5. 39 5. 18 4. 98 4. 79 4. 61 3 5403 99. 2 29. 5 16. 7 12. 1 9. 78 8. 45 7. 59 6. 99 6. 55 6. 22 5. 95 5. 74 5. 56 5. 42 5. 29 5. 18 5. 09 5. 01 4. 94 4. 87 4. 82 4. 76 4. 72 4. 68 4. 51 4. 31 4. 13 3. 95 3. 78 4 5625 99. 2 28. 7 16. 0 11. 4 9. 15 7. 85 7. 01 6. 42 5. 99 5. 67 5. 41 5. 21 5. 04 4. 89 4. 77 4. 67 4. 58 4. 50 4. 43 4. 37 4. 31 4. 26 4. 22 4. 18 4. 02 3. 83 3. 65 3. 48 3. 32 5 5764 99. 3 28. 2 15. 5 11. 0 8. 75 7. 46 6. 63 6. 06 5. 64 5. 32 5. 06 4. 86 4. 69 4. 56 4. 44 4. 34 4. 25 4. 17 4. 10 4. 04 3. 99 3. 94 3. 90 3. 85 3. 70 3. 51 3. 34 3. 17 3. 02 6 5859 99. 27. 9 15. 2 10. 7 8. 47 7. 19 6. 37 5. 80 5. 39 5. 07 4. 82 4. 62 4. 46 4. 32 4. 20 4. 10 4. 01 3. 94 3. 87 3. 81 3. 76 3. 71 3. 67 3. 63 3. 47 3. 29 3. 12 2. 96 2. 80 7 5928 99. 4 27. 7 15. 0 10. 5 8. 26 6. 99 6. 18 5. 61 5. 20 4. 89 4. 64 4. 44 4. 28 4. 14 4. 03 3. 93 3. 84 3. 77 3. 70 3. 64 3. 59 3. 54 3. 50 3. 46 3. 30 3. 12 2. 95 2. 79 2. 64 8 5981 99. 4 27. 5 14. 8 10. 3 8. 10 6. 84 6. 03 5. 47 5. 06 4. 74 4. 50 4. 30 4. 14 4. 00 3. 89 3. 79 3. 71 3. 63 3. 56 3. 51 3. 45 3. 41 3. 36 3. 32 3. 17 2. 99 2. 82 2. 66 2. 51 9 6022 99. 4 27. 3 14. 7 10. 2 7. 98 6. 72 5. 91 5. 35 4. 94 4. 63 4. 39 4. 19 4. 03 3. 89 3. 78 3. 68 3. 0 3. 52 3. 46 3. 40 3. 35 3. 30 3. 26 3. 22 3. 07 2. 89 2. 72 2. 56 2. 41 10 6056 99. 4 27. 2 14. 5 10. 1 7. 87 6. 62 5. 81 5. 26 4. 85 4. 54 4. 30 4. 10 3. 94 3. 80 3. 69 3. 59 3. 51 3. 43 3. 37 3. 31 3. 26 3. 21 3. 17 3. 13 2. 98 2. 80 2. 63 2. 47 2. 32 12 6106 99. 4 27. 1 14. 4 9. 89 7. 72 6. 47 5. 67 5. 11 4. 71 4. 40 4. 16 3. 96 3. 80 3. 67 3. 55 3. 46 3. 37 3. 30 3. 23 3. 17 3. 12 3. 07 3. 03 2. 99 2. 84 2. 66 2. 50 2. 34 2. 18 15 6157 99. 4 26. 9 14. 2 9. 72 7. 56 6. 31 5. 52 4. 96 4. 56 4. 25 4. 01 3. 82 3. 66 3. 52 3. 41 3. 31 3. 23 3. 15 3. 09 3. 03 2. 98 2. 93 2. 89 2. 85 2. 70 2. 52 2. 35 2. 19 2. 04 20 6209 99. 4 26. 14. 0 9. 55 7. 40 6. 16 5. 36 4. 81 4. 41 4. 10 3. 86 3. 66 3. 51 3. 37 3. 26 3. 16 3. 08 3. 00 2. 94 2. 88 2. 83 2. 78 2. 74 2. 70 2. 55 2. 37 2. 20 2. 03 1. 88 24 6235 99. 5 26. 6 13. 9 9. 47 7. 31 6. 07 5. 28 4. 73 4. 33 4. 02 3. 78 3. 59 3. 43 3. 29 3. 18 3. 08 3. 00 2. 92 2. 86 2. 80 2. 75 2. 70 2. 66 2. 62 2. 47 2. 29 2. 12 1. 95 1. 79 30 6261 99. 5 26. 5 13. 8 9. 38 7. 23 5. 99 5. 20 4. 65 4. 25 3. 94 3. 70 3. 51 3. 35 3. 21 3. 10 3. 00 2. 92 2. 84 2. 78 2. 72 2. 67 2. 62 2. 58 2. 54 2. 39 2. 20 2. 03 1. 86 1. 70 40 6287 99. 5 26. 4 13. 7 9. 29 7. 14 5. 91 5. 12 4. 57 4. 17 3. 86 3. 62 3. 43 3. 27 3. 13 3. 02 2. 92 2. 84 2. 6 2. 69 2. 64 2. 58 2. 54 2. 49 2. 45 2. 30 2. 11 1. 94 1. 76 1. 59 Degrees of Freedom for the Denominator 274 Appendixes Appendix H Critical Values of Chi-Square This table contains the values of of degrees of freedom. 2 that correspond to a specific right-tail area and specific number Example: With 17 df and a . 02 area in the upper tail, 2 30. 995 0 Degrees of Freedom, df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2 Right-Tail Area 0. 10 2. 706 4. 605 6. 251 7. 779 9. 236 10. 645 12. 017 13. 362 14. 684 15. 987 17. 275 18. 549 19. 812 21. 064 22. 307 23. 542 24. 769 25. 989 27. 204 28. 12 29. 615 30. 813 32. 007 33. 196 34. 382 35. 563 36. 741 37. 916 39. 087 40. 256 0. 05 3. 841 5. 991 7. 815 9. 488 11. 070 12. 592 14. 067 15. 507 16. 919 18. 307 19. 675 21. 026 22. 362 23. 685 24. 996 26. 296 27. 587 28. 869 30. 144 31. 410 32. 671 33. 924 35. 172 36. 415 37. 652 38. 885 40. 113 41. 337 42. 557 43. 773 0. 02 5. 412 7. 824 9. 837 11. 668 13. 388 15. 033 16. 622 18. 168 19. 679 21. 161 22. 618 24. 054 25. 472 26. 873 28. 259 29. 633 30. 995 32. 346 33. 687 35. 020 36. 343 37. 659 38. 968 40. 270 41. 566 42. 856 44. 140 45. 419 46. 693 47. 962 0. 01 6. 635 9. 210 11. 345 13. 277 15. 086 16. 812 18. 475 20. 090 21. 66 23. 209 24. 725 26. 217 27. 688 29. 141 30. 578 32. 000 33. 409 34. 805 36. 191 37. 566 38. 932 40. 289 41. 638 42. 980 44. 314 45. 642 46. 963 48. 278 49. 588 50. 892 Tables and Data Sets 275 Appendix I Binomial Probability Distribution n x 0 1 0. 05 0. 950 0. 050 0. 10 0. 900 0. 100 0. 20 0. 800 0. 200 0. 30 0. 700 0. 300 0. 40 0. 600 0. 400 1 0. 50 0. 500 0. 500 0. 60 0. 400 0. 600 0. 70 0. 300 0. 700 0. 80 0. 200 0. 800 0. 90 0. 100 0. 900 0. 95 0. 050 0. 950 Probability n 2 Probability x 0 1 2 0. 05 0. 903 0. 095 0. 003 0. 10 0. 810 0. 180 0. 010 0. 20 0. 640 0. 320 0. 040 0. 30 0. 490 0. 420 0. 090 0. 40 0. 360 0. 480 0. 60 0. 50 0. 250 0. 500 0. 250 0. 60 0. 160 0. 480 0. 360 0. 70 0. 090 0. 420 0. 490 0. 80 0. 040 0. 320 0. 640 0. 90 0. 010 0. 180 0. 810 0. 95 0. 003 0. 095 0. 903 n 3 Probability x 0 1 2 3 0. 05 0. 857 0. 135 0. 007 0. 000 0. 10 0. 729 0. 243 0. 027 0. 001 0. 20 0. 512 0. 384 0. 096 0. 008 0. 30 0. 343 0. 441 0. 189 0. 027 0. 40 0. 216 0. 432 0. 288 0. 064 0. 50 0. 125 0. 375 0. 375 0. 125 0. 60 0. 064 0. 288 0. 432 0. 216 0. 70 0. 027 0. 189 0. 441 0. 343 0. 80 0. 008 0. 096 0. 384 0. 512 0. 90 0. 001 0. 027 0. 243 0. 729 0. 95 0. 000 0. 007 0. 135 0. 857 n 4 Probability x 0 1 2 3 4 0. 05 0. 815 0. 171 0. 014 0. 000 0. 000 0. 0 0. 656 0. 292 0. 049 0. 004 0. 000 0. 20 0. 410 0. 410 0. 154 0. 026 0. 002 0. 30 0. 240 0. 412 0. 265 0. 076 0. 008 0. 40 0. 130 0. 346 0. 346 0. 154 0. 026 0. 50 0. 063 0. 250 0. 375 0. 250 0. 063 0. 60 0. 026 0. 154 0. 346 0. 346 0. 130 0. 70 0. 008 0. 076 0. 265 0. 412 0. 240 0. 80 0. 002 0. 026 0. 154 0. 410 0. 410 0. 90 0. 000 0. 004 0. 049 0. 292 0. 656 0. 95 0. 000 0. 000 0. 014 0. 171 0. 815 n 5 Probability x 0 1 2 3 4 5 0. 05 0. 774 0. 204 0. 021 0. 001 0. 000 0. 000 0. 10 0. 590 0. 328 0. 073 0. 008 0. 000 0. 000 0. 20 0. 328 0. 410 0. 205 0. 051 0. 006 0. 000 0. 30 0. 168 0. 360 0. 309 0. 132 0. 028 0. 002 0. 40 0. 78 0. 259 0. 346 0. 230 0. 077 0. 010 0. 50 0. 031 0. 156 0. 313 0. 313 0. 156 0. 031 0. 60 0. 010 0. 077 0. 230 0. 346 0. 259 0. 078 0. 70 0. 002 0. 028 0. 132 0. 309 0. 360 0. 168 0. 80 0. 000 0. 006 0. 051 0. 205 0. 410 0. 328 0. 90 0. 000 0. 000 0. 008 0. 073 0. 328 0. 590 0. 95 0. 000 0. 000 0. 001 0. 021 0. 204 0. 774 n 6 Probability x 0 1 2 3 4 5 6 0. 05 0. 735 0. 232 0. 031 0. 002 0. 000 0. 000 0. 000 0. 10 0. 531 0. 354 0. 098 0. 015 0. 001 0. 000 0. 000 0. 20 0. 262 0. 393 0. 246 0. 082 0. 015 0. 002 0. 000 0. 30 0. 118 0. 303 0. 324 0. 185 0. 060 0. 010 0. 001 0. 40 0. 047 0. 187 0. 311 0. 276 0. 138 0. 037 0. 004 0. 0 0. 016 0. 094 0. 234 0. 313 0. 234 0. 094 0. 016 0. 60 0. 004 0. 037 0. 138 0. 276 0. 311 0. 187 0. 047 0. 70 0. 001 0. 010 0. 060 0. 185 0. 324 0. 303 0. 118 0. 80 0. 000 0. 002 0. 015 0. 082 0. 246 0. 393 0. 262 0. 90 0. 000 0. 000 0. 001 0. 015 0. 098 0. 354 0. 531 0. 95 0. 000 0. 000 0. 000 0. 002 0. 031 0. 232 0. 735 276 Appendixes Appendix I Binomial Probability Distribution (continued) n 7 Probability x 0 1 2 3 4 5 6 7 0. 05 0. 698 0. 257 0. 041 0. 004 0. 000 0. 000 0. 000 0. 000 0. 10 0. 478 0. 372 0. 124 0. 023 0. 003 0. 000 0. 000 0. 000 0. 20 0. 210 0. 367 0. 275 0. 115 0. 029 0. 004 0. 000 0. 000 0. 30 0. 082 0. 247 0. 18 0. 227 0. 097 0. 025 0. 004 0. 000 0. 40 0. 028 0. 131 0. 261 0. 290 0. 194 0. 077 0. 017 0. 002 0. 50 0. 008 0. 055 0. 164 0. 273 0. 273 0. 164 0. 055 0. 008 0. 60 0. 002 0. 017 0. 077 0. 194 0. 290 0. 261 0. 131 0. 028 0. 70 0. 000 0. 004 0. 025 0. 097 0. 227 0. 318 0. 247 0. 082 0. 80 0. 000 0. 000 0. 004 0. 029 0. 115 0. 275 0. 367 0. 210 0. 90 0. 000 0. 000 0. 000 0. 003 0. 023 0. 124 0. 372 0. 478 0. 95 0. 000 0. 000 0. 000 0. 000 0. 004 0. 041 0. 257 0. 698 n 8 Probability x 0 1 2 3 4 5 6 7 8 0. 05 0. 663 0. 279 0. 051 0. 005 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 430 0. 383 0. 149 0. 033 0. 005 0. 000 0. 000 0. 000 0. 00 0. 20 0. 168 0. 336 0. 294 0. 147 0. 046 0. 009 0. 001 0. 000 0. 000 0. 30 0. 058 0. 198 0. 296 0. 254 0. 136 0. 047 0. 010 0. 001 0. 000 0. 40 0. 017 0. 090 0. 209 0. 279 0. 232 0. 124 0. 041 0. 008 0. 001 0. 50 0. 004 0. 031 0. 109 0. 219 0. 273 0. 219 0. 109 0. 031 0. 004 0. 60 0. 001 0. 008 0. 041 0. 124 0. 232 0. 279 0. 209 0. 090 0. 017 0. 70 0. 000 0. 001 0. 010 0. 047 0. 136 0. 254 0. 296 0. 198 0. 058 0. 80 0. 000 0. 000 0. 001 0. 009 0. 046 0. 147 0. 294 0. 336 0. 168 0. 90 0. 000 0. 000 0. 000 0. 000 0. 005 0. 033 0. 149 0. 383 0. 430 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 005 0. 051 0. 279 0. 663 n 9 Probability x 1 2 3 4 5 6 7 8 9 0. 05 0. 630 0. 299 0. 063 0. 008 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 387 0. 387 0. 172 0. 045 0. 007 0. 001 0. 000 0. 000 0. 000 0. 000 0. 20 0. 134 0. 302 0. 302 0. 176 0. 066 0. 017 0. 003 0. 000 0. 000 0. 000 0. 30 0. 040 0. 156 0. 267 0. 267 0. 172 0. 074 0. 021 0. 004 0. 000 0. 000 0. 40 0. 010 0. 060 0. 161 0. 251 0. 251 0. 167 0. 074 0. 021 0. 004 0. 000 0. 50 0. 002 0. 018 0. 070 0. 164 0. 246 0. 246 0. 164 0. 070 0. 018 0. 002 0. 60 0. 000 0. 004 0. 021 0. 074 0. 167 0. 251 0. 251 0. 161 0. 060 0. 010 0. 70 0. 000 0. 000 0. 004 0. 021 0. 074 0. 172 0. 267 0. 267 0. 156 0. 040 0. 80 0. 00 0. 000 0. 000 0. 003 0. 017 0. 066 0. 176 0. 302 0. 302 0. 134 0. 90 0. 000 0. 000 0. 000 0. 000 0. 001 0. 007 0. 045 0. 172 0. 387 0. 387 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 008 0. 063 0. 299 0. 630 n 10 Probability x 0 1 2 3 4 5 6 7 8 9 10 0. 05 0. 599 0. 315 0. 075 0. 010 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 349 0. 387 0. 194 0. 057 0. 011 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 107 0. 268 0. 302 0. 201 0. 088 0. 026 0. 006 0. 001 0. 000 0. 000 0. 000 0. 30 0. 028 0. 121 0. 233 0. 267 0. 200 0. 103 0. 037 0. 009 0. 001 0. 000 0. 000 0. 40 0. 006 0. 040 0. 121 0. 215 0. 251 0. 01 0. 111 0. 042 0. 011 0. 002 0. 000 0. 50 0. 001 0. 010 0. 044 0. 117 0. 205 0. 246 0. 205 0. 117 0. 044 0. 010 0. 001 0. 60 0. 000 0. 002 0. 011 0. 042 0. 111 0. 201 0. 251 0. 215 0. 121 0. 040 0. 006 0. 70 0. 000 0. 000 0. 001 0. 009 0. 037 0. 103 0. 200 0. 267 0. 233 0. 121 0. 028 0. 80 0. 000 0. 000 0. 000 0. 001 0. 006 0. 026 0. 088 0. 201 0. 302 0. 268 0. 107 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 011 0. 057 0. 194 0. 387 0. 349 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 010 0. 075 0. 315 0. 599 Tables and Data Sets 277 Appendix I Binomial Probability Distribution (continued) n 11 Probability x 1 2 3 4 5 6 7 8 9 10 11 0. 05 0. 569 0. 329 0. 087 0. 014 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 314 0. 384 0. 213 0. 071 0. 016 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 086 0. 236 0. 295 0. 221 0. 111 0. 039 0. 010 0. 002 0. 000 0. 000 0. 000 0. 000 0. 30 0. 020 0. 093 0. 200 0. 257 0. 220 0. 132 0. 057 0. 017 0. 004 0. 001 0. 000 0. 000 0. 40 0. 004 0. 027 0. 089 0. 177 0. 236 0. 221 0. 147 0. 070 0. 023 0. 005 0. 001 0. 000 0. 50 0. 000 0. 005 0. 027 0. 081 0. 161 0. 226 0. 226 0. 161 0. 081 0. 027 0. 005 0. 000 0. 60 0. 000 0. 001 0. 005 0. 023 0. 070 0. 147 0. 221 0. 236 0. 177 0. 89 0. 027 0. 004 0. 70 0. 000 0. 000 0. 001 0. 004 0. 017 0. 057 0. 132 0. 220 0. 257 0. 200 0. 093 0. 020 0. 80 0. 000 0. 000 0. 000 0. 000 0. 002 0. 010 0. 039 0. 111 0. 221 0. 295 0. 236 0. 086 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 016 0. 071 0. 213 0. 384 0. 314 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 014 0. 087 0. 329 0. 569 n 12 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 0. 05 0. 540 0. 341 0. 099 0. 017 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 282 0. 377 0. 230 0. 085 0. 021 0. 004 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 069 0. 206 0. 83 0. 236 0. 133 0. 053 0. 016 0. 003 0. 001 0. 000 0. 000 0. 000 0. 000 0. 30 0. 014 0. 071 0. 168 0. 240 0. 231 0. 158 0. 079 0. 029 0. 008 0. 001 0. 000 0. 000 0. 000 0. 40 0. 002 0. 017 0. 064 0. 142 0. 213 0. 227 0. 177 0. 101 0. 042 0. 012 0. 002 0. 000 0. 000 0. 50 0. 000 0. 003 0. 016 0. 054 0. 121 0. 193 0. 226 0. 193 0. 121 0. 054 0. 016 0. 003 0. 000 0. 60 0. 000 0. 000 0. 002 0. 012 0. 042 0. 101 0. 177 0. 227 0. 213 0. 142 0. 064 0. 017 0. 002 0. 70 0. 000 0. 000 0. 000 0. 001 0. 008 0. 029 0. 079 0. 158 0. 231 0. 240 0. 168 0. 071 0. 014 0. 80 0. 000 0. 000 0. 000 0. 000 0. 001 0. 003 0. 016 0. 053 0. 133 0. 236 0. 83 0. 206 0. 069 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 004 0. 021 0. 085 0. 230 0. 377 0. 282 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 017 0. 099 0. 341 0. 540 n 13 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0. 05 0. 513 0. 351 0. 111 0. 021 0. 003 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 254 0. 367 0. 245 0. 100 0. 028 0. 006 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 055 0. 179 0. 268 0. 246 0. 154 0. 069 0. 023 0. 006 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 010 0. 054 0. 139 0. 218 0. 234 0. 180 0. 103 0. 044 0. 14 0. 003 0. 001 0. 000 0. 000 0. 000 0. 40 0. 001 0. 011 0. 045 0. 111 0. 184 0. 221 0. 197 0. 131 0. 066 0. 024 0. 006 0. 001 0. 000 0. 000 0. 50 0. 000 0. 002 0. 010 0. 035 0. 087 0. 157 0. 209 0. 209 0. 157 0. 087 0. 035 0. 010 0. 002 0. 000 0. 60 0. 000 0. 000 0. 001 0. 006 0. 024 0. 066 0. 131 0. 197 0. 221 0. 184 0. 111 0. 045 0. 011 0. 001 0. 70 0. 000 0. 000 0. 000 0. 001 0. 003 0. 014 0. 044 0. 103 0. 180 0. 234 0. 218 0. 139 0. 054 0. 010 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 006 0. 023 0. 069 0. 154 0. 246 0. 268 0. 179 0. 055 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 006 0. 028 0. 00 0. 245 0. 367 0. 254 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 003 0. 021 0. 111 0. 351 0. 513 278 Appendixes Appendix I Binomial Probability Distribution (continued) n 14 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0. 05 0. 488 0. 359 0. 123 0. 026 0. 004 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 229 0. 356 0. 257 0. 114 0. 035 0. 008 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 044 0. 154 0. 250 0. 250 0. 172 0. 086 0. 032 0. 009 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 007 0. 041 0. 113 0. 194 0. 229 0. 196 0. 26 0. 062 0. 023 0. 007 0. 001 0. 000 0. 000 0. 000 0. 000 0. 40 0. 001 0. 007 0. 032 0. 085 0. 155 0. 207 0. 207 0. 157 0. 092 0. 041 0. 014 0. 003 0. 001 0. 000 0. 000 0. 50 0. 000 0. 001 0. 006 0. 022 0. 061 0. 122 0. 183 0. 209 0. 183 0. 122 0. 061 0. 022 0. 006 0. 001 0. 000 0. 60 0. 000 0. 000 0. 001 0. 003 0. 014 0. 041 0. 092 0. 157 0. 207 0. 207 0. 155 0. 085 0. 032 0. 007 0. 001 0. 70 0. 000 0. 000 0. 000 0. 000 0. 001 0. 007 0. 023 0. 062 0. 126 0. 196 0. 229 0. 194 0. 113 0. 041 0. 007 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 009 0. 032 0. 086 0. 172 0. 250 0. 250 0. 154 0. 044 0. 90 0. 000 0. 000 0. 00 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 008 0. 035 0. 114 0. 257 0. 356 0. 229 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 004 0. 026 0. 123 0. 359 0. 488 n 15 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0. 05 0. 463 0. 366 0. 135 0. 031 0. 005 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 206 0. 343 0. 267 0. 129 0. 043 0. 010 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 035 0. 132 0. 231 0. 250 0. 188 0. 103 0. 043 0. 014 0. 003 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 005 0. 031 0. 092 0. 70 0. 219 0. 206 0. 147 0. 081 0. 035 0. 012 0. 003 0. 001 0. 000 0. 000 0. 000 0. 000 0. 40 0. 000 0. 005 0. 022 0. 063 0. 127 0. 186 0. 207 0. 177 0. 118 0. 061 0. 024 0. 007 0. 002 0. 000 0. 000 0. 000 0. 50 0. 000 0. 000 0. 003 0. 014 0. 042 0. 092 0. 153 0. 196 0. 196 0. 153 0. 092 0. 042 0. 014 0. 003 0. 000 0. 000 0. 60 0. 000 0. 000 0. 000 0. 002 0. 007 0. 024 0. 061 0. 118 0. 177 0. 207 0. 186 0. 127 0. 063 0. 022 0. 005 0. 000 0. 70 0. 000 0. 000 0. 000 0. 000 0. 001 0. 003 0. 012 0. 035 0. 081 0. 147 0. 206 0. 219 0. 170 0. 092 0. 031 0. 005 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 003 0. 014 0. 043 0. 03 0. 188 0. 250 0. 231 0. 132 0. 035 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 010 0. 043 0. 129 0. 267 0. 343 0. 206 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 005 0. 031 0. 135 0. 366 0. 463 n 16 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0. 05 0. 440 0. 371 0. 146 0. 036 0. 006 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 185 0. 329 0. 275 0. 142 0. 051 0. 014 0. 003 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 028 0. 113 0. 211 0. 246 0. 200 0. 120 0. 055 0. 20 0. 006 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 003 0. 023 0. 073 0. 146 0. 204 0. 210 0. 165 0. 101 0. 049 0. 019 0. 006 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 40 0. 000 0. 003 0. 015 0. 047 0. 101 0. 162 0. 198 0. 189 0. 142 0. 084 0. 039 0. 014 0. 004 0. 001 0. 000 0. 000 0. 000 0. 50 0. 000 0. 000 0. 002 0. 009 0. 028 0. 067 0. 122 0. 175 0. 196 0. 175 0. 122 0. 067 0. 028 0. 009 0. 002 0. 000 0. 000 0. 60 0. 000 0. 000 0. 000 0. 001 0. 004 0. 014 0. 039 0. 084 0. 142 0. 189 0. 198 0. 162 0. 101 0. 047 0. 015 0. 003 0. 000 0. 70 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 006 0. 019 0. 049 0. 01 0. 165 0. 210 0. 204 0. 146 0. 073 0. 023 0. 003 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 006 0. 020 0. 055 0. 120 0. 200 0. 246 0. 211 0. 113 0. 028 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 003 0. 014 0. 051 0. 142 0. 275 0. 329 0. 185 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 006 0. 036 0. 146 0. 371 0. 440 Tables and Data Sets 279 Appendix I Binomial Probability Distribution (continued) n 17 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0. 05 0. 418 0. 374 0. 158 0. 041 0. 008 0. 001 0. 000 0. 000 0. 00 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 167 0. 315 0. 280 0. 156 0. 060 0. 017 0. 004 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 023 0. 096 0. 191 0. 239 0. 209 0. 136 0. 068 0. 027 0. 008 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 002 0. 017 0. 058 0. 125 0. 187 0. 208 0. 178 0. 120 0. 064 0. 028 0. 009 0. 003 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 40 0. 000 0. 002 0. 010 0. 034 0. 080 0. 138 0. 184 0. 193 0. 161 0. 107 0. 057 0. 024 0. 008 0. 002 0. 000 0. 000 0. 000 0. 000 0. 50 0. 000 0. 000 0. 001 0. 005 0. 018 0. 47 0. 094 0. 148 0. 185 0. 185 0. 148 0. 094 0. 047 0. 018 0. 005 0. 001 0. 000 0. 000 0. 60 0. 000 0. 000 0. 000 0. 000 0. 002 0. 008 0. 024 0. 057 0. 107 0. 161 0. 193 0. 184 0. 138 0. 080 0. 034 0. 010 0. 002 0. 000 0. 70 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 003 0. 009 0. 028 0. 064 0. 120 0. 178 0. 208 0. 187 0. 125 0. 058 0. 017 0. 002 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 008 0. 027 0. 068 0. 136 0. 209 0. 239 0. 191 0. 096 0. 023 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 004 0. 017 0. 060 0. 156 0. 280 0. 315 0. 167 0. 95 0. 000 0. 000 0. 00 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 008 0. 041 0. 158 0. 374 0. 418 n 18 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0. 05 0. 397 0. 376 0. 168 0. 047 0. 009 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 150 0. 300 0. 284 0. 168 0. 070 0. 022 0. 005 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 018 0. 081 0. 172 0. 230 0. 215 0. 151 0. 082 0. 035 0. 012 0. 003 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 002 0. 013 0. 046 0. 105 0. 168 0. 202 0. 87 0. 138 0. 081 0. 039 0. 015 0. 005 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 40 0. 000 0. 001 0. 007 0. 025 0. 061 0. 115 0. 166 0. 189 0. 173 0. 128 0. 077 0. 037 0. 015 0. 004 0. 001 0. 000 0. 000 0. 000 0. 000 0. 50 0. 000 0. 000 0. 001 0. 003 0. 012 0. 033 0. 071 0. 121 0. 167 0. 185 0. 167 0. 121 0. 071 0. 033 0. 012 0. 003 0. 001 0. 000 0. 000 0. 60 0. 000 0. 000 0. 000 0. 000 0. 001 0. 004 0. 015 0. 037 0. 077 0. 128 0. 173 0. 189 0. 166 0. 115 0. 061 0. 025 0. 007 0. 001 0. 000 0. 70 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 005 0. 015 0. 039 0. 081 0. 138 0. 187 0. 202 0. 168 0. 105 0. 046 0. 013 0. 02 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 003 0. 012 0. 035 0. 082 0. 151 0. 215 0. 230 0. 172 0. 081 0. 018 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 005 0. 022 0. 070 0. 168 0. 284 0. 300 0. 150 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 009 0. 047 0. 168 0. 376 0. 397 280 Appendixes Appendix I Binomial Probability Distribution (continued) n 19 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0. 05 0. 377 0. 377 0. 179 0. 053 0. 011 0. 002 0. 000 0. 000 0. 000 0. 000 0. 00 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 135 0. 285 0. 285 0. 180 0. 080 0. 027 0. 007 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 014 0. 068 0. 154 0. 218 0. 218 0. 164 0. 095 0. 044 0. 017 0. 005 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 001 0. 009 0. 036 0. 087 0. 149 0. 192 0. 192 0. 153 0. 098 0. 051 0. 022 0. 008 0. 002 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 40 0. 000 0. 001 0. 005 0. 017 0. 047 0. 093 0. 145 0. 180 0. 180 0. 146 0. 098 0. 053 0. 024 0. 008 0. 002 0. 001 0. 000 0. 000 0. 00 0. 000 0. 50 0. 000 0. 000 0. 000 0. 002 0. 007 0. 022 0. 052 0. 096 0. 144 0. 176 0. 176 0. 144 0. 096 0. 052 0. 022 0. 007 0. 002 0. 000 0. 000 0. 000 0. 60 0. 000 0. 000 0. 000 0. 000 0. 001 0. 002 0. 008 0. 024 0. 053 0. 098 0. 146 0. 180 0. 180 0. 145 0. 093 0. 047 0. 017 0. 005 0. 001 0. 000 0. 70 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 002 0. 008 0. 022 0. 051 0. 098 0. 153 0. 192 0. 192 0. 149 0. 087 0. 036 0. 009 0. 001 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 005 0. 017 0. 044 0. 095 0. 164 0. 218 0. 218 0. 154 0. 068 0. 014 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 00 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 007 0. 027 0. 080 0. 180 0. 285 0. 285 0. 135 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 011 0. 053 0. 179 0. 377 0. 377 n 20 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0. 05 0. 358 0. 377 0. 189 0. 060 0. 013 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 122 0. 270 0. 285 0. 190 0. 090 0. 032 0. 009 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 012 0. 58 0. 137 0. 205 0. 218 0. 175 0. 109 0. 055 0. 022 0. 007 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 001 0. 007 0. 028 0. 072 0. 130 0. 179 0. 192 0. 164 0. 114 0. 065 0. 031 0. 012 0. 004 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 40 0. 000 0. 000 0. 003 0. 012 0. 035 0. 075 0. 124 0. 166 0. 180 0. 160 0. 117 0. 071 0. 035 0. 015 0. 005 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 50 0. 000 0. 000 0. 000 0. 001 0. 005 0. 015 0. 037 0. 074 0. 120 0. 160 0. 176 0. 160 0. 120 0. 074 0. 037 0. 015 0. 005 0. 001 0. 000 0. 000 0. 000 0. 60 0. 000 0. 000 0. 000 0. 000 0. 000 0. 01 0. 005 0. 015 0. 035 0. 071 0. 117 0. 160 0. 180 0. 166 0. 124 0. 075 0. 035 0. 012 0. 003 0. 000 0. 000 0. 70 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 004 0. 012 0. 031 0. 065 0. 114 0. 164 0. 192 0. 179 0. 130 0. 072 0. 028 0. 007 0. 001 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 007 0. 022 0. 055 0. 109 0. 175 0. 218 0. 205 0. 137 0. 058 0. 012 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 009 0. 032 0. 090 0. 190 0. 285 0. 270 0. 122 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 00 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 013 0. 060 0. 189 0. 377 0. 358 Tables and Data Sets 281 Appendix I Binomial Probability Distribution (concluded) n 25 Probability x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0. 05 0. 277 0. 365 0. 231 0. 093 0. 027 0. 006 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 10 0. 072 0. 199 0. 266 0. 226 0. 138 0. 065 0. 024 0. 007 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 20 0. 004 0. 24 0. 071 0. 136 0. 187 0. 196 0. 163 0. 111 0. 062 0. 029 0. 012 0. 004 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 30 0. 000 0. 001 0. 007 0. 024 0. 057 0. 103 0. 147 0. 171 0. 165 0. 134 0. 092 0. 054 0. 027 0. 011 0. 004 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 40 0. 000 0. 000 0. 000 0. 002 0. 007 0. 020 0. 044 0. 080 0. 120 0. 151 0. 161 0. 147 0. 114 0. 076 0. 043 0. 021 0. 009 0. 003 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 50 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 005 0. 014 0. 032 0. 061 0. 097 0. 133 0. 55 0. 155 0. 133 0. 097 0. 061 0. 032 0. 014 0. 005 0. 002 0. 000 0. 000 0. 000 0. 000 0. 000 0. 60 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 003 0. 009 0. 021 0. 043 0. 076 0. 114 0. 147 0. 161 0. 151 0. 120 0. 080 0. 044 0. 020 0. 007 0. 002 0. 000 0. 000 0. 000 0. 70 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 004 0. 011 0. 027 0. 054 0. 092 0. 134 0. 165 0. 171 0. 147 0. 103 0. 057 0. 024 0. 007 0. 001 0. 000 0. 80 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 004 0. 012 0. 029 0. 062 0. 111 0. 163 0. 196 0. 187 0. 136 0. 71 0. 024 0. 004 0. 90 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 002 0. 007 0. 024 0. 065 0. 138 0. 226 0. 266 0. 199 0. 072 0. 95 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 006 0. 027 0. 093 0. 231 0. 365 0. 277 282 Appendixes Appendix J Factors for Control Charts Chart for Averages Factors for Control Limits Chart for Ranges Factors for Central Line Factors for Control Limits Number of Items in Sample, n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 SOURCE: Adapted

A2 1. 880 1. 023 . 729 . 577 . 483 . 419 . 373 . 337 . 308 . 285 . 266 . 249 . 235 . 223 d2 1. 128 1. 693 2. 059 2. 326 2. 534 2. 704 2. 847 2. 970 3. 078 3. 173 3. 258 3. 336 3. 407 3. 472 D3 0 0 0 0 0 . 076 . 136 . 184 . 223 . 256 . 284 . 308 . 329 . 348 D4 3. 267 2. 575 2. 282 2. 115 2. 004 1. 924 1. 864 1. 816 1. 777 1. 744 1. 716 1. 692 1. 671 1. 652 from American Society for Testing and Materials, Manual on Quality Control of Materials, 1951, Table B2, p. 115. For a more detailed table and explanation, see Acheson, J. Duncan, Quality Control and Industrial Statistics, 3d ed. (Homewood, Ill. : Richard D. Irwin, 1974), Table M, p. 27. Tables and Data Sets 283 Appendix K Poisson Distribution x 0 1 2 3 4 5 6 7 0. 1 0. 9048 0. 0905 0. 0045 0. 0002 0. 0000 0. 0000 0. 0000 0. 0000 0. 2 0. 8187 0. 1637 0. 0164 0. 0011 0. 0001 0. 0000 0. 0000 0. 0000 0. 3 0. 7408 0. 2222 0. 0333 0. 0033 0. 0003 0. 0000 0. 0000 0. 0000 0. 4 0. 6703 0. 2681 0. 0536 0. 0072 0. 0007 0. 0001 0. 0000 0. 0000 0. 5 0. 6065 0. 3033 0. 0758 0. 0126 0. 0016 0. 0002 0. 0000 0. 0000 0. 6 0. 5488 0. 3293 0. 0988 0. 0198 0. 0030 0. 0004 0. 0000 0. 0000 0. 7 0. 4966 0. 3476 0. 1217 0. 0284 0. 0050 0. 0007 0. 0001 0. 0000 0. 8 0. 4493 0. 3595 0. 1438 0. 0383 0. 0077 0. 0012 0. 0002 0. 000 0. 9 0. 4066 0. 3659 0. 1647 0. 0494 0. 0111 0. 0020 0. 0003 0. 0000 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 1. 0 0. 3679 0. 3679 0. 1839 0. 0613 0. 0153 0. 0031 0. 0005 0. 0001 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 2. 0 0. 1353 0. 2707 0. 2707 0. 1804 0. 0902 0. 0361 0. 0120 0. 0034 0. 0009 0. 0002 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 3. 0 0. 0498 0. 1494 0. 2240 0. 2240 0. 1680 0. 1008 0. 0504 0. 0216 0. 0081 0. 0027 0. 0008 0. 0002 0. 0001 0. 000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 4. 0 0. 0183 0. 0733 0. 1465 0. 1954 0. 1954 0. 1563 0. 1042 0. 0595 0. 0298 0. 0132 0. 0053 0. 0019 0. 0006 0. 0002 0. 0001 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 5. 0 0. 0067 0. 0337 0. 0842 0. 1404 0. 1755 0. 1755 0. 1462 0. 1044 0. 0653 0. 0363 0. 0181 0. 0082 0. 0034 0. 0013 0. 0005 0. 0002 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 6. 0 0. 0025 0. 0149 0. 0446 0. 0892 0. 1339 0. 1606 0. 1606 0. 1377 0. 1033 0. 0688 0. 0413 0. 0225 0. 0113 0. 0052 0. 0022 0. 0009 0. 0003 0. 0001 0. 0000 0. 0000 0. 0000 0. 000 0. 0000 7. 0 0. 0009 0. 0064 0. 0223 0. 0521 0. 0912 0. 1277 0. 1490 0. 1490 0. 1304 0. 1014 0. 0710 0. 0452 0. 0263 0. 0142 0. 0071 0. 0033 0. 0014 0. 0006 0. 0002 0. 0001 0. 0000 0. 0000 0. 0000 8. 0 0. 0003 0. 0027 0. 0107 0. 0286 0. 0573 0. 0916 0. 1221 0. 1396 0. 1396 0. 1241 0. 0993 0. 0722 0. 0481 0. 0296 0. 0169 0. 0090 0. 0045 0. 0021 0. 0009 0. 0004 0. 0002 0. 0001 0. 0000 9. 0 0. 0001 0. 0011 0. 0050 0. 0150 0. 0337 0. 0607 0. 0911 0. 1171 0. 1318 0. 1318 0. 1186 0. 0970 0. 0728 0. 0504 0. 0324 0. 0194 0. 0109 0. 0058 0. 0029 0. 0014 0. 0006 0. 0003 0. 0001 284 Appendixes Appendix L Table of Random Numbers 2711 94873 54921 77640 61545 17147 13748 87455 08999 78804 82173 97594 73881 46071 44492 31864 51574 35350 46943 22665 39437 77082 24544 27503 24590 48155 20226 70178 10169 81084 69202 80561 08199 98883 84568 04269 10538 77843 12034 10524 68935 89450 90696 49006 74591 06315 62386 86848 65643 11084 08182 90935 78680 97636 00835 19519 04742 14813 57409 81333 26921 25168 67176 22912 19686 72170 90692 76132 36502 87226 97957 47784 25649 15558 24545 86226 53752 73444 41465 03701 20777 95787 26703 28220 69286 35173 13124 24955 94636 72829 76632 65665 20451 32047 87025 17012 09184 82122 69480 46534 75997 31684 06635 37397 93251 22497 92460 50373 91185 53809 28472 89178 93504 90326 12495 37722 43339 92925 01172 33304 11838 40098 43370 37738 06435 40359 90648 38790 51935 28598 21727 89426 95128 39358 76054 95745 36099 25900 49455 47641 46984 29190 24211 93086 52368 77103 62092 04028 46598 78957 79866 63952 98689 93379 87203 16857 85801 28037 10200 32471 98958 68190 42636 42453 93135 55794 65689 92124 46045 57975 10433 97962 28007 24849 52758 28723 24362 53626 05711 70013 81511 93325 48599 53720 21615 53893 13140 63843 76362 93315 61772 43709 97310 00112 59416 00968 46617 36959 04501 77353 58095 09865 17306 56454 36759 42426 53444 91182 61411 46034 07960 05043 38233 88108 95185 14636 76539 92634 46991 03985 21564 89845 06779 70722 45685 15364 83314 93780 09799 3794 51887 86412 09333 80161 80883 86022 37706 95029 83532 80875 92786 11172 60446 20470 34417 07235 99419 87827 40403 39578 83319 14491 25170 59818 49197 84822 65626 32786 23392 36306 66124 17407 16154 72064 77799 05148 27909 35681 33804 21566 51570 28392 72402 71859 90151 69125 00014 18629 79077 53169 16175 57479 12584 83371 36797 77722 44562 93859 31062 28090 22651 34481 73530 17136 70557 10728 64230 12813 91408 77868 80295 99518 65928 45827 85967 92598 58710 65261 47797 22498 89731 48201 96451 58601 52441 54505 05467 43690 80006 65796 73558 78187 62632 83736 46516 12609 19207 68766 88159 97054 53746 54194 24374 15181 82845 52498 57179 93634 69903 97728 07086 95977 62865 28255 86746 42189 95034 08627 32343 22970 79741 93394 87709 74164 01704 49186 55406 11173 56377 19239 95069 83917 57925 32357 88272 50113 21727 89136 35542 72915 27495 06112 53956 06016 49644 57171 69413 24371 33437 60303 46516 52153 31232 11131 39139 84193 44693 20205 91186 52560 89754 47535 96574 86328 55809 33292 85481 80699 48130 84349 74599 34691 30533 71666 19634 88247 17173 34376 71635 85428 18625 11413 29667 90610 22024 21119 51141 35599 61056 81466 34533 08169 24709 94397 92686 86857 97016 74639 68519 23259 70339 19197 61782 12219 90900 22448 67877 66294 65768 34937 44143 25658 13829 07293 53628 51487 07857 13345 49303 09184 84379 14985 89736 46977 21898 39967 69776 36408 08601 55721 92405 72920 30859 32921 80631 25228 72949 84138 75666 89205 57808 11261 06978 12529 84870 31702 86290 30782 03040 96196 62727 81877 44032 55920 18172 22571 01549 41218 55949 79548 97687 73898 72226 38809 12000 64443 42510 51695 90689 70603 Tables and Data Sets 285 Appendix M Wilcoxon T Values 2 . 15 . 10 . 050 0 2 3 5 8 10 13 17 21 25 30 35 41 47 53 60 67 75 83 91 100 110 119 130 140 151 163 175 187 200 213 286 466 690 960 1,276 1,638 2,045 . 05 . 025 . 04 . 020 . 03 . 015 . 02 . 010 . 01 . 005 n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 50 60 70 80 90 100 .075 0 1 2 4 7 9 12 16 19 24 28 33 39 45 51 58 65 73 81 89 98 108 118 128 138 150 161 173 186 199 212 226 302 487 718 995 1,318 1,688 2,105 2 3 5 8 10 13 17 21 25 29 34 40 46 52 58 65 73 81 89 98 107 116 126 137 147 159 170 182 195 264 434 648 907 1,211 1,560 1,955 0 1 3 5 7 9 12 16 19 23 28 33 38 43 50 56 63 70 78 86 94 103 112 122 132 143 154 165 177 189 257 425 636 891 1,192 1,537 1,928 0 2 4 6 8 11 14 18 21 26 30 35 41 47 53 59 66 74 82 90 99 108 117 127 137 148 159 171 182 249 413 620 872 1,168 1,509 1,894 0 1 3 5 7 9 12 15 19 23 27 32 37 43 49 55 62 69 76 84 92 101 110 120 130 140 151 162 173 238 397 600 846 1,136 1,471 1,850 0 1 3 5 7 9 12 15 19 23 27 32 37 42 48 54 61 68 75 83 91 100 109 118 128 138 148 159 220 373 567 805 1,086 1,410 1,779 SOURCE: Abridged from Robert L.

McCormack, “Extended Tables of the Wilcoxon Matched-Pair Signed Rank Statistic,” Journal of the American Statistical Association, September 1965, pp. 866–67. 286 Appendixes Appendix N Banking Data Set — Case x1 x2 x3 x4 x5 x6 Account balance in $ Number of ATM transactions in the month Number of other bank services used Has a debit card (1 yes, 0 no) yes, 0 no) Receives interest on the account (1 City where banking is done x1 1,756 748 1,501 1,831 1,622 1,886 740 1,593 1,169 2,125 1,554 1,474 1,913 1,218 1,006 2,215 137 167 343 2,557 2,276 1,494 2,144 1,995 1,053 1,526 1,120 1,838 1,746 1,616 1,958 634 580 1,320 1,675 x2 13 9 10 10 14 17 6 10 6 18 12 12 6 10 12 20 7 5 7 20 15 11 17 10 8 8 8 7 11 10 6 2 4 4 6 x3 4 2 1 4 6 3 3 8 4 6 6 7 5 3 4 3 2 4 2 7 4 2 3 7 4 4 6 5 2 4 2 7 1 5 7 x4 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 x5 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 x6 2 1 1 3 4 1 3 1 4 2 3 1 1 1 1 4 3 4 1 4 3 1 3 2 3 2 3 3 2 2 2 4 1 1 2 Tables and Data Sets 287 Appendix N Banking Data Set — Case (concluded) x1 789 1,735 1,784 1,326 2,051 1,044 1,885 1,790 765 1,645 32 1,266 890 2,204 2,409 1,338 2,076 1,708 2,138 2,375 1,455 1,487 1,125 1,989 2,156 x2 8 12 11 16 14 7 10 11 4 6 2 11 7 14 16 14 12 13 18 12 9 8 6 12 14 x3 4 7 5 8 4 5 6 4 3 9 0 7 1 5 8 4 5 3 5 4 5 4 4 3 5 x4 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 x5 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 x6 4 3 1 3 4 1 2 3 4 4 3 4 1 2 2 2 2 1 4 2 3 4 2 2 2

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