Page 1 of5

UNIVERSITY OF SWAZILAND

F ACUL TY OF SOCIAL SCIENCES

DEPARTMENT OF STATISTICS AND DEMOGRAPHY

SUPPLEMENTARY EXAMINATION 201718

COURSE TITI~E INFERENTIAL STATISTICS I

COURSE CODE STA 232ST 232

TIME ALLOWED THREE (3) HOURS

INSTRUCTION ANSWER ALL QUESTIONS IN SECTION A amp

ANY THREE QUESTIONS IN SECTION B

SPECIAL REQUIREMENTS SCIENTIFIC CALCULATORS AND STATISTICAL

TABLES

DO NOT OPEN THIS PAGE UNTIL PERMISSION HAS BEEN GRANTED BY TIlE

INVIGILATOR

Page 2 of5 Question 1

The pass rate for a certain course is 65 From a random sample of fifty students in this course X is the number failing the course Determine

a) P(X ~ 25) b) P(X lt 25) c) P(20 lt X lt 30) (3+3+4 marks)

Question 2

In the course of three days 210 car accidents occurred within a certain municipal area These accidents are divided into

Fatal Serious Minor No Total (deaths) injuries injuries injuries

3 12 23 172 210

a) Estimate the proportion of accidents in the municipal area that (i) resulted in no injuries and (ii) were fatal

b) What are the standard errors of the estimations in (a) c) If the data above is representative of traffic accidents in the area for the whole month find for the

month a 95 confidence interval for the proportion of accidents that did not result in injuries (2+2+2+4 marks)

Question 3

All newly appointed representatives at a firm are required to complete a two-week compulsory training course in sales techniques The course has been presented for ten years at a current cost of E3000 per person A consultant approaches the firm and offers to train newly appointed staff with the aid of a modern course in sales techniques at a total estimated cost of E5 000 per person This course also lasts for two weeks The firms board of directors has to decide whether the newly appointed representatives would take the traditional course in sales techniques or would instead change to a new course offered by the consultant Suppose the first-year sales figures often representatives selected at random who completed the new course are as follows

R287900 R419400 R338300 R287500 R310850 R292600 R390050 R369850 R430400 R338450

It follows that x = R346 530 and s R53 76758 Suppose the firms decision is based on a choice between the following two hypotheses

HoJ1 = 300000 againstH1 J1 gt 300 000

with 300 000 being the mean first-year sales of representative who completed the traditional course What would be your conclusions (10 marks)

Page 3 of5 Question 4

An insurance company investigates various methods of cutting down on operating costs One problem is the excessively high monthly telephone account A preliminary analysis of the account shows that more than half of the outgoing calls are non-official Since unmarried staff members are suspected of being largely responsible a random sample is drawn from married and unmarried staff without the knowledge of either group The following table is a summary of the sample information with regard to the total duration of private calls made in one month

Staff Sample size __M=e=an--____V---ari=a=nc=e Single n1=65 x1=525 sf = 145 Marrie~__--llamp==90____ _--x~2=---3gtlt8--9__---s-i_=-1~37__~_

Test at a 5 level of significance to see if on average private calls by unmarried persons last longer than those by married persons (10 marks)

Question 5

Assume a government agency desires to estimate the miles per gallon that a particular new (make and

model) car is capable of attaining To do this the agency acquires one of these cars fills the gas tank

and then a trained driver drives the car for 100 miles the gas tank is then refilled and the same driver

drives the car 100 miles at which time it is again refilled and driven 100 miles and so on This

operation is performed a total of n = 10 times the number of gallons needed to fill the gas tank these

10 times are 478442394415490392394468432423

Assuming these values constitute a random sample from a normal population with mean fl and variance a-

(a) Compute estimates for 11 and a (b) Compute the 90 confidence limits for f the number of gallons needed to drive the car a 100

miles (10 marks)

Question 6

A bag contains 10 flashbulbs 8 of which are good If 5 flashbulbs are chosen from the bag at random what is the probability function for the number of good flashbulbs For the number of bad bulbs

(10 marks)

SECTION B

Question 7

(a) In a certain region of the country it is known from past experience that the probability of selecting

an n adult over 40 years of age with cancer is 005 If the probability of a doctor correctly diagnosing

a person with cancer as having the disease is 078 and the probability of incorrectly diagnosing a

person without cancer as having cancer is 006 (8 marks)

(i) What is the probability that a person is diagnosed as having cancer

(ii) What is the probability that a person diagnosed as having cancer actually has the disease

Page 2 of5 Question 1

The pass rate for a certain course is 65 From a random sample of fifty students in this course X is the number failing the course Determine

a) P(X ~ 25) b) P(X lt 25) c) P(20 lt X lt 30) (3+3+4 marks)

Question 2

In the course of three days 210 car accidents occurred within a certain municipal area These accidents are divided into

Fatal Serious Minor No Total (deaths) injuries injuries injuries

3 12 23 172 210

a) Estimate the proportion of accidents in the municipal area that (i) resulted in no injuries and (ii) were fatal

b) What are the standard errors of the estimations in (a) c) If the data above is representative of traffic accidents in the area for the whole month find for the

month a 95 confidence interval for the proportion of accidents that did not result in injuries (2+2+2+4 marks)

Question 3

All newly appointed representatives at a firm are required to complete a two-week compulsory training course in sales techniques The course has been presented for ten years at a current cost of E3000 per person A consultant approaches the firm and offers to train newly appointed staff with the aid of a modern course in sales techniques at a total estimated cost of E5 000 per person This course also lasts for two weeks The firms board of directors has to decide whether the newly appointed representatives would take the traditional course in sales techniques or would instead change to a new course offered by the consultant Suppose the first-year sales figures often representatives selected at random who completed the new course are as follows

R287900 R419400 R338300 R287500 R310850 R292600 R390050 R369850 R430400 R338450

It follows that x = R346 530 and s R53 76758 Suppose the firms decision is based on a choice between the following two hypotheses

HoJ1 = 300000 againstH1 J1 gt 300 000

with 300 000 being the mean first-year sales of representative who completed the traditional course What would be your conclusions (10 marks)

Page 3 of5 Question 4

An insurance company investigates various methods of cutting down on operating costs One problem is the excessively high monthly telephone account A preliminary analysis of the account shows that more than half of the outgoing calls are non-official Since unmarried staff members are suspected of being largely responsible a random sample is drawn from married and unmarried staff without the knowledge of either group The following table is a summary of the sample information with regard to the total duration of private calls made in one month

Staff Sample size __M=e=an--____V---ari=a=nc=e Single n1=65 x1=525 sf = 145 Marrie~__--llamp==90____ _--x~2=---3gtlt8--9__---s-i_=-1~37__~_

Test at a 5 level of significance to see if on average private calls by unmarried persons last longer than those by married persons (10 marks)

Question 5

Assume a government agency desires to estimate the miles per gallon that a particular new (make and

model) car is capable of attaining To do this the agency acquires one of these cars fills the gas tank

and then a trained driver drives the car for 100 miles the gas tank is then refilled and the same driver

drives the car 100 miles at which time it is again refilled and driven 100 miles and so on This

operation is performed a total of n = 10 times the number of gallons needed to fill the gas tank these

10 times are 478442394415490392394468432423

Assuming these values constitute a random sample from a normal population with mean fl and variance a-

(a) Compute estimates for 11 and a (b) Compute the 90 confidence limits for f the number of gallons needed to drive the car a 100

miles (10 marks)

Question 6

A bag contains 10 flashbulbs 8 of which are good If 5 flashbulbs are chosen from the bag at random what is the probability function for the number of good flashbulbs For the number of bad bulbs

(10 marks)

SECTION B

Question 7

(a) In a certain region of the country it is known from past experience that the probability of selecting

an n adult over 40 years of age with cancer is 005 If the probability of a doctor correctly diagnosing

a person with cancer as having the disease is 078 and the probability of incorrectly diagnosing a

person without cancer as having cancer is 006 (8 marks)

(i) What is the probability that a person is diagnosed as having cancer

(ii) What is the probability that a person diagnosed as having cancer actually has the disease

Page 3 of5 Question 4

An insurance company investigates various methods of cutting down on operating costs One problem is the excessively high monthly telephone account A preliminary analysis of the account shows that more than half of the outgoing calls are non-official Since unmarried staff members are suspected of being largely responsible a random sample is drawn from married and unmarried staff without the knowledge of either group The following table is a summary of the sample information with regard to the total duration of private calls made in one month

Staff Sample size __M=e=an--____V---ari=a=nc=e Single n1=65 x1=525 sf = 145 Marrie~__--llamp==90____ _--x~2=---3gtlt8--9__---s-i_=-1~37__~_

Test at a 5 level of significance to see if on average private calls by unmarried persons last longer than those by married persons (10 marks)

Question 5

Assume a government agency desires to estimate the miles per gallon that a particular new (make and

model) car is capable of attaining To do this the agency acquires one of these cars fills the gas tank

and then a trained driver drives the car for 100 miles the gas tank is then refilled and the same driver

drives the car 100 miles at which time it is again refilled and driven 100 miles and so on This

operation is performed a total of n = 10 times the number of gallons needed to fill the gas tank these

10 times are 478442394415490392394468432423

Assuming these values constitute a random sample from a normal population with mean fl and variance a-

(a) Compute estimates for 11 and a (b) Compute the 90 confidence limits for f the number of gallons needed to drive the car a 100

miles (10 marks)

Question 6

A bag contains 10 flashbulbs 8 of which are good If 5 flashbulbs are chosen from the bag at random what is the probability function for the number of good flashbulbs For the number of bad bulbs

(10 marks)

SECTION B

Question 7

(a) In a certain region of the country it is known from past experience that the probability of selecting

an n adult over 40 years of age with cancer is 005 If the probability of a doctor correctly diagnosing

a person with cancer as having the disease is 078 and the probability of incorrectly diagnosing a

person without cancer as having cancer is 006 (8 marks)

(i) What is the probability that a person is diagnosed as having cancer

(ii) What is the probability that a person diagnosed as having cancer actually has the disease

Page 4 ofS

(b )An agriculturist claims that she has cultivated a new variety of orange that has a significantly

higher content of ascorbic acid (vitamin C) than the variety that is the current top seller The

accompanying data shows the ascorbic acid content (mgl1 OOg) for a random sample of fifteen oranges of the new variety and twelve of the current top seller

Ascorbic content of two varieties of

951 917

904 901 964 936

Lets fl1 and fl2 indicate the population mean ascorbic acid content of the new variety and of the current top seller Test the claim made by the agriculturist at 1 significance level

(12 marks)

Question 8

The data in the following table was collected lIsing completely randomised design Achievement scores for fOllr different groups of students each group taught by a different teaching technique The objective of the experiment was to test the hypothesis of no difference in the population distributions of achievement test scores versus the alternative that they differ in location that is at least one of the distributions is shifted above the others Conduct the test using the Kruskal-Wallis test using a ~~ 005

1 2 3 4

65

87

73

79

81

69

75

69

83

81

72

79

90

59

78

67

62

83

76

94

89

80

88

(20 marks)

Page 5 of5 Question 9

A survey was conducted among 400 affluent Americans with household incomes of$750 000 or

more per year to examine the relationship between the use of a financial advisor and ownership of

stocks The results ofthe survey are retlected in the following table

Use financial advisor Yes 165 135

At 5 significance level can you conclude that the use of a financial advisor is independent of stock ownership for all affluent Americans (20 marks)

Question 10

The numbers of incoming phone calls at a company switchboard during I-minute intervals are

believed to have a Poisson distribution Use a=O1 0 and the following data to test the assumption that

the incoming phone calls follow a Poisson distribution (20 marks)

Number of incoming phone calls

During I-minute Interval Observed Frequencv

o 15

31

2 20

3 15

4 13

5 4

Total 100

END OF EXAM

STATISTICAL TABLES Cumulative normal distribution

Critical values of the distribution

Critical values of the F distribution

Critical values of the chi-squared distribution

copy C Dougherty 20012002 (cdougllertylseacuk) These tables have been computed to accompany the text C Dougherty Introduction to Econometrics (second edition 2002 Oxford University Press Oxford) They may be reproduced freely provided that this attribution Is retained

Page 5 of5 Question 9

A survey was conducted among 400 affluent Americans with household incomes of$750 000 or

more per year to examine the relationship between the use of a financial advisor and ownership of

stocks The results ofthe survey are retlected in the following table

Use financial advisor Yes 165 135

At 5 significance level can you conclude that the use of a financial advisor is independent of stock ownership for all affluent Americans (20 marks)

Question 10

The numbers of incoming phone calls at a company switchboard during I-minute intervals are

believed to have a Poisson distribution Use a=O1 0 and the following data to test the assumption that

the incoming phone calls follow a Poisson distribution (20 marks)

Number of incoming phone calls

During I-minute Interval Observed Frequencv

o 15

31

2 20

3 15

4 13

5 4

Total 100

END OF EXAM

STATISTICAL TABLES Cumulative normal distribution

Critical values of the distribution

Critical values of the F distribution

Critical values of the chi-squared distribution

copy C Dougherty 20012002 (cdougllertylseacuk) These tables have been computed to accompany the text C Dougherty Introduction to Econometrics (second edition 2002 Oxford University Press Oxford) They may be reproduced freely provided that this attribution Is retained

STATISTICAL TABLES Cumulative normal distribution

Critical values of the distribution

Critical values of the F distribution

Critical values of the chi-squared distribution

copy C Dougherty 20012002 (cdougllertylseacuk) These tables have been computed to accompany the text C Dougherty Introduction to Econometrics (second edition 2002 Oxford University Press Oxford) They may be reproduced freely provided that this attribution Is retained

STATISTICAL TABLES 1 y~Ii

TABLE A1

Cumulative Standardized Normal Distribution

A(z) is the integral of the standardized nonnal distribution from- co to z (in other words the area under the curve to the left of z) It gives the probahlity of a nonnal random variable not being more than z standard deviations above its mean Values of z of particular importance

z A(z) 1645 09500 Lower limit of right 5 tail 1960 09750 Lower limit of right 25 tail 2326 09900 Lower limit of right 1 tail 2576 09950 Lower limit of right 05 tail 3090 09990 Lower limit of right 01 tail 3291 09995 Lower limit of right 0 05 tail

-4 -3 3 4

z 000 001 002 003 004 005 006 007 008 009

00 05000 05040 05080 05120 05160 05199 05239 05279 05319 05359 01 05398 05438 05478 05517 05557 05596 05636 05675 05714 05753 02 05793 05832 05871 05910 05948 05987 06026 06064 06103 06141 03 06179 06217 9middot6255 06293 06331 06368 06406 06443 06480 06517 04 06554 06591 06628 06664 06700 06736 06772 06808 06844 06879 05 06915 06950 06985 07019 07054 07088 07123 07157 07190 07224 06 07257 07291 07324 07357 07389 07422 07454 07486 07517 07549 07 07580 07611 07642 07673 07704 07734 07764 07794 07823 07852 I 08 07881 07910 07939 07967 07995 08023 08051 08078 08106 08133 I

09 08159 08186 08212 08238 08264 08289 08315 08340 08365 08389 10 08413 08438 08461 08485 08508 08531 08554 08577 08599 08621 11 08643 08665 08686 08708 08729 08749 08770 08790 08810 08830 12 08849 08869 08888 08907 08925 08944 08962 08980 08997 09015 13 09032 09049 09066 09082 09099 09115 09131 09147 09162 09177 14 09192 09207 09222 09236 09251 09265 09279 09292 09306 09319 15 09332 09345 09357 09370 09382 09394 09406 09418 09429 09441 16 09452 09463 09474 09484 09495 09505 09515 09525 09535 09545 17 09554 09564 09573 09582 09591 09599 09608 09616 09625 09633 18 09641 09649 096S6 09664 09671 09678 09686 09693 09699 09706 19 09713 09719 09726 09732 09738 09744 09750 09756 09761 09767 20 09772 09778 09783 09788 09793 09798 09803 09808 09812 09817 21 09821 09826 09830 09834 09838 09842 09846 09850 09854 09857 22 09861 09864 09868 09871 09875 09878 09881 09884 09887 09890 23 09893 09896 09898 09901 09904 09906 09909 09911 09913 09916 24 09918 09920 09922 09925 09927 09929 09931 09932 09934 09936 25 09938 09940 09941 09943 09945 09946 09948 09949 09951 09952 26 09953 09955 09956 09957 09959 09960 09961 09962 09963 09964 27 09965 09966 09967 09968 09969 09970 09971 09972 09973 09974 28 09974 09975 09976 09977 09977 09978 09979 09979 09980 09981 29 09981 09982 09982 09983 09984 09984 09985 09985 09986 09986 30 09987 09987 09987 09988 09988 09989 09989 09989 09990 09990 31 09990 09991 09991 09991 09992 09992 09992 09992 09993 09993 32 09993 09993 09994 09994 09994 09994 09994 09995 09995 09995 33 09995 09995 09995 09996 09996 09996 09996 09996 09996 09997 34 09997 09997 09997 09997 09997 09997 09997 09997 09997 09998 35 09998 09998 09998 09998 09998 09998 09998 09998 09998 09998 36 09998 09998 09999

t Table cum prob t 50 t75 tso t85 t~o t~5 t ~75 (99 t~~5 t~99 t99~5

one-tail 050 025 020 015 010 005 0025 001 0005 0001 000051

two-tails 100 050 040 030 020 010 005 002 001 0002 0001

3182 6965

tmiddottablexls 7142007

STATISTICAL TABLES 3 oF i ~_

TABLE A3middot

F Distribution Critical Values of F (5 significance level)

2VI 1 3 4 5 6 7 8 9 10 12 14 16 18 20 Vz

1 16145 19950 21571 22458 23016 23399 2367723888 24054 24188 24391 24536 24646 24732 24801 2 1851 1900 1916 1925 1930 1933 1935 1937 1938 1940 1941 1942 1943 1944 1945 3 1013 955 928 912 901 894 889 885 881 879 874 871 869 g67 866 4 771 694 659 639 626 616 609 604 600 596 591 587 584 582 580 5 661 579 541 519 505 495 488 482 477 474 468 464 460 458 456

6 599 514 476 453 439 428 421 415 410 406 400 396 392 390 387 7 559 474 435 412 397 387 379 373 368 364 357 353 349 347 344 8 532 446 407 384 369 358 350 344 339 335 328 324 320 317 315 9 512 426 386 363 348 337 329 323 318 314 307 303 299 296 294

10 496 410 371 348 333 322 314 307 302 298 291 286 283 280 277

11 484 398 359 336 320 309 301 295 290 285 279 274 270 267 265 12 475 389 349 326 311 300 291 285 280 275 269 264 260 257 254 13 467 381 341 318 303 292 283 277 271 267 260 255 251 248 246 14 460 374 middot334 311 296 285 276 270 265 260 253 248 244 241 239 15 454 368 329 306 290 279 271 264 259 254 248 242 238 235 233

16 449 363 324 301 285 274 266 259 254 249 242 237 233 230 228 17 445 359 320 296 281 270 261 255 249 245 238 233 229 226 223 18 441 355 316 293 277 266 258 251 246 241 234 229 225 222 219 19 438 352 3l3 290 274 263 254 248 242 238 231 226 221 218middot 216 20 435 349 310 287 271 260 251 245 239 235 228 222 218 215 212

21 432 347 307 284 268 257 249 242 237 232 225 220 216 212 210 22 430 344 305 282 266 255 246 240 234 230 223 217 213 210 207 23 428 342 303 280 264 253 244 237 232 227 220 215 211 208 205 24 426 340 301 278 262 251 242 236 230 225 218 213 209 205 203 25 424 339 middot299 276 260 249 240 234 228 224 216 211 207 204 201

26 422 337 298 274 259 241 239 232 227 222 215 209 205 202 199 27 421 335 296 273 257 246 237 231 225 220 213 208 204 200 197 28 420 334 295 271 256 245 236 229 224 219 212 206 202 199 196 29 418 333 293 270 255 243 235 228 222 218 210 205 201 197 194 30 417 332 292 269 253 242 233 227 221 216 209 204 199 196 193

35 412 327 287 264 249 237 229 222 216 211 204 199 194 191 188 40 408 323 284 261 245 234 225 218 212 208 200 195 190 187 184 50 403 318 279 256 240 229 220 213 207 203 195 189 185 181 178 60 400 315 276 253 237 225 217 210 204 199 192 186 182 178 175 70 398 313 274 250 235 223 214 207 202 197 189 184 179 175 172

80 396 311 272 249 233 221 213 206 200 195 188 182 177 173 170 90 395 310 271 247 232 220 211 204 199 194 186 180 176 172 169

100 394 309 270 246 231 219 210 203 197 193 185 179 175 171 168 120 392 307 268 245 229 218 209 202 196 191 183 178 173 169 166 150 390 306 266 243 227 216 207 200 194 189 182 176 171 167 164

200 389 304 265 242 226 214 206 198 193 188 180 174 169 166 162 250 388 303 264 241 225 213 205 198 192 187 179 173 168 165 161 300 387 303 263 240 224 213 204 197 191 186 178 172 168 164 161 400 386 302 263 239 224 212 203 196 190 185 178 172 167 163 160 500 386 301 262 239 223 212 203 196 190 185 177 171 166 162 159

600 386 301 262 239 223 211 202 195 190 185 177 171 166 162 159 750 385 301 262 238 223 211 202 195 189 184 177 170 166 162 158

1000 385 300 261 238 222 211 202 195 189 184 176 170 165 161 158

t Table cum prob t 50 t75 tso t85 t~o t~5 t ~75 (99 t~~5 t~99 t99~5

one-tail 050 025 020 015 010 005 0025 001 0005 0001 000051

two-tails 100 050 040 030 020 010 005 002 001 0002 0001

3182 6965

tmiddottablexls 7142007

STATISTICAL TABLES 3 oF i ~_

TABLE A3middot

F Distribution Critical Values of F (5 significance level)

2VI 1 3 4 5 6 7 8 9 10 12 14 16 18 20 Vz

1 16145 19950 21571 22458 23016 23399 2367723888 24054 24188 24391 24536 24646 24732 24801 2 1851 1900 1916 1925 1930 1933 1935 1937 1938 1940 1941 1942 1943 1944 1945 3 1013 955 928 912 901 894 889 885 881 879 874 871 869 g67 866 4 771 694 659 639 626 616 609 604 600 596 591 587 584 582 580 5 661 579 541 519 505 495 488 482 477 474 468 464 460 458 456

6 599 514 476 453 439 428 421 415 410 406 400 396 392 390 387 7 559 474 435 412 397 387 379 373 368 364 357 353 349 347 344 8 532 446 407 384 369 358 350 344 339 335 328 324 320 317 315 9 512 426 386 363 348 337 329 323 318 314 307 303 299 296 294

10 496 410 371 348 333 322 314 307 302 298 291 286 283 280 277

11 484 398 359 336 320 309 301 295 290 285 279 274 270 267 265 12 475 389 349 326 311 300 291 285 280 275 269 264 260 257 254 13 467 381 341 318 303 292 283 277 271 267 260 255 251 248 246 14 460 374 middot334 311 296 285 276 270 265 260 253 248 244 241 239 15 454 368 329 306 290 279 271 264 259 254 248 242 238 235 233

16 449 363 324 301 285 274 266 259 254 249 242 237 233 230 228 17 445 359 320 296 281 270 261 255 249 245 238 233 229 226 223 18 441 355 316 293 277 266 258 251 246 241 234 229 225 222 219 19 438 352 3l3 290 274 263 254 248 242 238 231 226 221 218middot 216 20 435 349 310 287 271 260 251 245 239 235 228 222 218 215 212

21 432 347 307 284 268 257 249 242 237 232 225 220 216 212 210 22 430 344 305 282 266 255 246 240 234 230 223 217 213 210 207 23 428 342 303 280 264 253 244 237 232 227 220 215 211 208 205 24 426 340 301 278 262 251 242 236 230 225 218 213 209 205 203 25 424 339 middot299 276 260 249 240 234 228 224 216 211 207 204 201

26 422 337 298 274 259 241 239 232 227 222 215 209 205 202 199 27 421 335 296 273 257 246 237 231 225 220 213 208 204 200 197 28 420 334 295 271 256 245 236 229 224 219 212 206 202 199 196 29 418 333 293 270 255 243 235 228 222 218 210 205 201 197 194 30 417 332 292 269 253 242 233 227 221 216 209 204 199 196 193

35 412 327 287 264 249 237 229 222 216 211 204 199 194 191 188 40 408 323 284 261 245 234 225 218 212 208 200 195 190 187 184 50 403 318 279 256 240 229 220 213 207 203 195 189 185 181 178 60 400 315 276 253 237 225 217 210 204 199 192 186 182 178 175 70 398 313 274 250 235 223 214 207 202 197 189 184 179 175 172

80 396 311 272 249 233 221 213 206 200 195 188 182 177 173 170 90 395 310 271 247 232 220 211 204 199 194 186 180 176 172 169

100 394 309 270 246 231 219 210 203 197 193 185 179 175 171 168 120 392 307 268 245 229 218 209 202 196 191 183 178 173 169 166 150 390 306 266 243 227 216 207 200 194 189 182 176 171 167 164

200 389 304 265 242 226 214 206 198 193 188 180 174 169 166 162 250 388 303 264 241 225 213 205 198 192 187 179 173 168 165 161 300 387 303 263 240 224 213 204 197 191 186 178 172 168 164 161 400 386 302 263 239 224 212 203 196 190 185 178 172 167 163 160 500 386 301 262 239 223 212 203 196 190 185 177 171 166 162 159

600 386 301 262 239 223 211 202 195 190 185 177 171 166 162 159 750 385 301 262 238 223 211 202 195 189 184 177 170 166 162 158

1000 385 300 261 238 222 211 202 195 189 184 176 170 165 161 158

STATISTICAL TABLES 3 oF i ~_

TABLE A3middot

F Distribution Critical Values of F (5 significance level)

2VI 1 3 4 5 6 7 8 9 10 12 14 16 18 20 Vz

1 16145 19950 21571 22458 23016 23399 2367723888 24054 24188 24391 24536 24646 24732 24801 2 1851 1900 1916 1925 1930 1933 1935 1937 1938 1940 1941 1942 1943 1944 1945 3 1013 955 928 912 901 894 889 885 881 879 874 871 869 g67 866 4 771 694 659 639 626 616 609 604 600 596 591 587 584 582 580 5 661 579 541 519 505 495 488 482 477 474 468 464 460 458 456

6 599 514 476 453 439 428 421 415 410 406 400 396 392 390 387 7 559 474 435 412 397 387 379 373 368 364 357 353 349 347 344 8 532 446 407 384 369 358 350 344 339 335 328 324 320 317 315 9 512 426 386 363 348 337 329 323 318 314 307 303 299 296 294

10 496 410 371 348 333 322 314 307 302 298 291 286 283 280 277

11 484 398 359 336 320 309 301 295 290 285 279 274 270 267 265 12 475 389 349 326 311 300 291 285 280 275 269 264 260 257 254 13 467 381 341 318 303 292 283 277 271 267 260 255 251 248 246 14 460 374 middot334 311 296 285 276 270 265 260 253 248 244 241 239 15 454 368 329 306 290 279 271 264 259 254 248 242 238 235 233

16 449 363 324 301 285 274 266 259 254 249 242 237 233 230 228 17 445 359 320 296 281 270 261 255 249 245 238 233 229 226 223 18 441 355 316 293 277 266 258 251 246 241 234 229 225 222 219 19 438 352 3l3 290 274 263 254 248 242 238 231 226 221 218middot 216 20 435 349 310 287 271 260 251 245 239 235 228 222 218 215 212

21 432 347 307 284 268 257 249 242 237 232 225 220 216 212 210 22 430 344 305 282 266 255 246 240 234 230 223 217 213 210 207 23 428 342 303 280 264 253 244 237 232 227 220 215 211 208 205 24 426 340 301 278 262 251 242 236 230 225 218 213 209 205 203 25 424 339 middot299 276 260 249 240 234 228 224 216 211 207 204 201

26 422 337 298 274 259 241 239 232 227 222 215 209 205 202 199 27 421 335 296 273 257 246 237 231 225 220 213 208 204 200 197 28 420 334 295 271 256 245 236 229 224 219 212 206 202 199 196 29 418 333 293 270 255 243 235 228 222 218 210 205 201 197 194 30 417 332 292 269 253 242 233 227 221 216 209 204 199 196 193

35 412 327 287 264 249 237 229 222 216 211 204 199 194 191 188 40 408 323 284 261 245 234 225 218 212 208 200 195 190 187 184 50 403 318 279 256 240 229 220 213 207 203 195 189 185 181 178 60 400 315 276 253 237 225 217 210 204 199 192 186 182 178 175 70 398 313 274 250 235 223 214 207 202 197 189 184 179 175 172

80 396 311 272 249 233 221 213 206 200 195 188 182 177 173 170 90 395 310 271 247 232 220 211 204 199 194 186 180 176 172 169

100 394 309 270 246 231 219 210 203 197 193 185 179 175 171 168 120 392 307 268 245 229 218 209 202 196 191 183 178 173 169 166 150 390 306 266 243 227 216 207 200 194 189 182 176 171 167 164

200 389 304 265 242 226 214 206 198 193 188 180 174 169 166 162 250 388 303 264 241 225 213 205 198 192 187 179 173 168 165 161 300 387 303 263 240 224 213 204 197 191 186 178 172 168 164 161 400 386 302 263 239 224 212 203 196 190 185 178 172 167 163 160 500 386 301 262 239 223 212 203 196 190 185 177 171 166 162 159

600 386 301 262 239 223 211 202 195 190 185 177 171 166 162 159 750 385 301 262 238 223 211 202 195 189 184 177 170 166 162 158

1000 385 300 261 238 222 211 202 195 189 184 176 170 165 161 158

STATISTICAL TABLES -shyi_- 1~

4 ~

TABLE A3 (continued)

F Distribution Critical Values of F (5 significance level)

VI 25 30 3S 40 50 60 7S 100 150 200 Vz

1 2492625010250692511425177 25220 25262 25304 25346 25368 2 1946 1946 1947 1947 1948 1948 1948 1949 1949 1949 3 863 862 860 859 858 857 856 855 854 854 4 577 575 573 572 570 569 568 566 565 565 5 452 450 448 446 444 443 442 441 439 439

i

6 7

8 9

10

383 340 311 289 273

381 338 308 286 270

379 336 306 284 268

377 334 304 283 266

375 332 302 280 264

374 330 301 279 262

373 329 299 277 260

371 327 297 276 259

370 326 296 274 257

369 325 295 273 256

11 260 12 250 13 241 14 234 15 228

257 247 238 231 225

255 244 236 228 222

253 243 234 227 220

251 240 231 224 218

249 238 230 222 216

247 237 228 221 214

246 235 226 219 212

244 233 224 217 210

243 232 223 216 210

16 17 18 19 20

223 218 214 211 207

219 215 211 207 204

217 212 208 205 201

215 210 206 203 199

212 208 204 200 197

211 206 202 198 195

209 204 200 196 193

207 202 198 194 191

205 200 196 192 189

204 199 195 191 188

21 22 23 24 25

205 202 200 197 196

201 198 196 194

192

198 196 193 191 189

196 194 191 189 187

194 191 188 186 184

192 189 186 184 182

190 187 184 182 180

188 185 182 180 178

middot186 183 180 178 176

184 182 179 177 175

26 27 28 29 30

194 192 191 189 188

190 188 187 185 184

187 186 184 183 181

185 184 182 181 179

182 181 179 177 176

180 179 t77 175 174

178 176 175 173 172

176 174 173 171 170

174 172 170 169 167

173 171 169 167 166

35 40 50 60 70

182 178 173 169 166

179 174 169 165 162

176 172 166 162 159

174 169 163 159 157

170 166 160 156 153

168 164 158 153 150

166 161 155 151 148

163 159 152 148 145

161 156 150 145 142

160 155 148 144 140

80 90

100 120 150

164 163 162 160 158

160 159 157 155 154

157 155 154

middot152 150

154 153 152 150 148

151 149 148 146 144

148 146 145

143 141

145 144 142 140 138

143 141 139 137 134

139 138 136 133 131

138 136 134 132 129

200 250 300 400 500

156 155 154 153 153

152 150 150 149 148

148 147 146 145 145

146 144 143 142 142

141 140 139 138 138

139 137 136 135 135

135 134 133 132 131

132 131 130 128 128

128 127 126 124 123

126 125 123 122 121

600 750

1000

152 152 152

148 147 147

144 144 143

141 141 141

137 137 136

134 134 133

131 130 130

middot127 126 126

123 122 122

120 120 119

5

STATISTICAL TABLES ~ middottt t

TABLE A3 (continued)

F Distribution Critical Values of F (1 significance level)

VI 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 12

1 405218 499950 540335 562458 576365 585899 592836 598107 602247 605585 610632 614267 617010 619153 620873

2 9850 9900 9917 9925 9930 9933 9936 9937 9939 9940 9942 9943 9944 9944 9945 3 3412 3082 2946 2871 2824 2791 2767 2749 2735 2723 2705 2692 2683 2675 2669 4 2120 1800 1669 1598 1552 1521 1498 1480 1466 1455 1437 1425 1415 1408 1402 5 1626 1327 1206 1139 1097 1067 1046 1029 1016 1005 989 977 968 961 955

6 1375 1092 978 915 875 847 826 810 798 787 772 760 752 745 740 7 1225 955 845 785 746 719 699 684 672 662 647 636 628 621 616 8 1126 865 759 701 663 637 618 603 591 581 567 556 548 541 536 9 1056 802 699 642 606 580 561 547 535 526 511 501 492 486 481

10 1004 756 655 599 564 539 520 506 494 485 471 460 452 446 441

11 965 721 622 567 532 507 489 474 463 454 440 429 421 415 410 12 933 693 595 541 506 482 464 450 439 430 416 405 397 391 386 13 907 670 574 521 486 462 444 430 419 410 396 386 378 372 366 14 886 651 556 504 469 446 428 414 403 394 380 370 362 356 351 15 868 636 542 489 456 432 414 400 389 380 367 356 349 342 337

16 853 623 529 477 444 420 403 389 378 369 355 345 337 331 326 17 840 611 518 467 434 410 393 379 368 359 346 335 327 321 316 18 829 601 509 458 425 401 384 371 360 351 337 327 319 313 308 19 818 593 501 450 417 394 377 363 352 343 330 319 312 305 300 20 810 585 494 443 410 387 370 356 346 337 323 313 305 299 294

21 802 578 487 437 404 381 364 351 340 331 317 307 299 293 288 22 795 572 482 431 399 376 359 345 335 326 312 302 294 288 283 23 788 566 476 426 394 371 354 341 330 321 307 297 289 283 278 24 782 561 472 422 390 367 350 336 326 317 303 293 285 279 274 25 777 557 468 418 385 363 346 332 322 313 299 289 281 275 270

26 772 553 464 414 382 359 342 329 318 309 296 286 278 272 266 27 768 549 460 411 378 356 339 326 315 306 293 282 275 268 263 28 764 545 457 407 375 353 336 323 312 303 290 279 272 265 260 29 760 542 454 404 373 350 333 320 309 300 287 277 269 263 257 30 756 539 451 402 370 347 330 317 307 298 284 274 266 260 255

35 742 527 440 391 359 337 320 307 296 288 274 264 256 250 244 40 731 518 431 383 351 329 312 299 289 280 266 256 248 242 237 50 717 506 420 372 341 319 302 289 278 270 256 246 238 232 227 60 708 498 413 365 334 312 295 282 272 263 250 239 231 225 220 70 701 492 407 360 329 307 291 278 267 259 245 235 227 220 215

80 696 488 404 356 326 304 287 274 264 255 242 231 223 217 212 90 693 485 401 353 323 301 284 272 261 252 239 229 221 214 209

100 690 482 398 351 321 299 282 269 259 250 237 227 219 212 207 120 685 479 395 348 317 296 279 266 256 247 234 223 215 209 203 150 681 475 391 345 314 292 276 263 253 244 231 220 212 206 200

200 676 471 388 341 311 289 273 260 250 241 227 217 209 203 197 250 674 469 386 340 309 287 271 258 248 239 226 215 207 201 195 300 672 468 385 338 308 286 270 257 247 238 224 214 206 199 194 400 670 466 383 337 306 285 268 256 245 237 223 213 205 198 192 500 669 465 382 336 305 284 268 255 244 236 222 212 204 197 192

600 668 464 381 335 305 283 267 254 244 235 221 211 203 196 191 750 667 463 381 334 304 283 266 253 243 234 221 211 202 196 190

1000 666 463 380 334 304 282 266 253 243 234 220 210 202 195 190

STATISTICAL TABLES

d litimiddot 6

TABLE A3 (continued)

F Distribution Critical Values of F (1 significance level)

Vi 25 30 35 40 50 60 75 100 150 200 V2

1 623983 626065 627557 628678 630252 631303 632356 633411 634468 634997 2 9946 9947 9947 9947 9948 9948 9949 9949 9949 9949 3 2658 2650 2645 2641 2635 2632 2628 2624 2620 2618 4 1391 1384 1379 1375 1369 1365 1361 1358 1354 1352 5 945 938 933 929 924 920 917 913 909 908

6 730 723 718 714 709 706 702 699 695 693 7 606 599 594 591 586 582 579 575 572 570 8 526 520 515 512 507 503 500 496 493 491 9 471 465 460 457 452 448 445 441 438 436

10 431 425 420 417 412 408 405 401 398 396

11 401 394 389 386 381 378 374 371 367 366 12 376 370 365 362 357 354 350 347 343 341 13 357 351 346 343 338 334 331 327 324 322 14 341 335 330 327 322 318 315 311 308 306 15 328 321 317 313 308 305 301 298 294 292

16 316 310 305 302 297 293 290 286 283 281 17 307 300 296 292 287 283 280 276 273 271 18 298 292 287 284 278 275 271 268 264 262 19 291 284 280 276 271 267 264 260 257 255 20 284 278 273 269 264 261 257 254 250 248

21 279 272 267 264 258 255 251 248 244 242 22 273 267 262 258 253 250 246 242 238 236 23 269 262 257 254 248 245 241 237 234 232 24 264 258 253 249 244 240 237 233 229 227 25 260 254 249 245 240 236 233 229 225 223

26 257 250 245 242 236 233 229 225 221 219 27 254 247 242 238 233 229 226 222 218 216 28 251 244 239 235 230 226 223 219 215 213 29 248 241 236 233 227 223 220 216 212 210 30 245 239 234 230 225 221 217 213 209 207

35 235 228 223 219 214 210 206 202 198 196 40 227 220 215 211 206 202 198 194 190 187 50 217 210 205 201 195 191 187 182 178 176 60 210 203 198 194 188 184 179 175 170 168 70 205 198 193 189 183 178 174 170 165 162

80 201 194 189 185 179 175 170 165 161 158 90 199 192 186 182 176 172 167 162 157 155

100 197 189 184 180 174 169 165 160 155 152 120 193 186 181 176 170 166 161 156 151 148 150 190 183 177 173 166 162 157 152 146 143

200 187 179 174 169 163 158 153 148 142 139 250 185 177 172 167 161 156 151 146 140 136 300 184 176 170 166 159 155 150 144 138 135 400 182 175 169 164 158 153 148 142 136 132 500 181 174 i68 163 157 152 147 141 134 131

600 180 173 167 163 156 151 146 140 134 130 750 180 172 166 162 155 150 145 139 133 129

1000 179 172 166 161 154 150 144 138 132 128

middot STATISTICAL TABLES 7 -t11

TABLE A3 (continued)

F Distribution Critical Values of F(O1 significance level)

VI 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 Vz

1 405e05 500e05 540005 562005 576e05 586e05 593e05 598e05 602e05 606e05 611005 614e05 617e05 619005 621e05

2 99850 99900 99917 99925 99930 99933 99936 99937 99939 99940 99942 99943 99944 99944 99945 3 16703 14850 14111 13710 13458 13285 13158 13062 12986 12925 12832 12764 12714 12674 12642 4 7414 6125 5618 5344 5171 5053 4966 4900 4847 4805 4741 4695 4660 4632 4610 5 47183712 3320 3109 2975 2883 2816 2765 2724 2692 2642 2606 2578 2557 2539

6 3551 2700 2370 2192 2080 2003 1946 1903 1869 1841 1799 1768 1745 1727 1712 7 2925 2169 1877 1720 1621 1552 1502 1463 1433 1408 1371 1343 1323 1306 1293 8 2541 1849 1583 1439 1348 1286 1240 1205 1177 1154 1119 1094 1075 1060 1048 9 2286 1639 1390 1256 1171 1113 1070 1037 1011 989 957 933 915 901 890

10 2104 1491 1255 1128 1048 993 952 920 896 875 845 822 805 791 780

11 1969 1381 1156 1035 958 905 866 835 812 792 763 741 724 711 701 12 1864 1297 1080 963 889 838 800 771 748 729 700 679 663 651 640 13 1782 1231 1021 907 835 786 749 721 698 680 652 631 616 603 593 14 1714 1178 973 862 792 744 708 680 658 640 613 593 578 566 556 15 1659 1134 934 825 757 709 674 647 626 608 581 562 546 535 525

16 1612 1097 901 794 727 680 646 619 598 581 555 535 520 509 499 17 1572 1066 873 768 702 656 622 596 575 558 532 513 499 487 478 18 1538 1039 849 746 681 635 602 576 556 539 513 494 480 468 459 19 1508 1016 828 127 662 618 585 559 539 522 497 478 464 452 443 20 1482 995 810 710 646 602 569 544 524 508 482 464 449 438 429

21 1459 977 794 695 632 588 556 531 511 495 470 451 437 426 417 22 1438 961 780 681 619 576 544 519 499 483 458 440 426 415 406 23 1420 947 767 670 608 565 533 509 489 473 448 430 416 405 396 24 1403 934 755 659 598 555 523 499 480 464 439 421 407 396 387 25 1388 922 745 649 589 546 515 491 471 456 431 413 399 388 379

26 1374 912 736 641 580 538 507 483 464 448 424 406 392 381 372 27 1361 902 727 633 573 531 500 476 457 441 417 399 386 375 366 28 1350 893 719 625 566 524 493 469 450 435 411 393 380 369 360 29 1339 885 712 619 559 518 487 464 445 429 405 388 374 363 354 30 1329 877 705 612 553 512 482 458 439 424 400 382 369 358 349

35 1290 847 679 588 530 489 459 436 418 403 379 362 348 338 329 40 1261 825 659 570 513 473 444 421 402 387 364 347 334 323 314 50 1222 796 634 546 490 451 422 400 382 367 344 327 341 304 295 60 1197 777 617 531 476 437 409 386 369 354 332 315 302 291 283 70 1180 764 606 520 466 428 399 377 360 345 323 306 293 283 274

80 1167 754 597 512 458 420 392 370 353 339 316 300 287 276 268 90 1157 747 591 506 453 415 387 365 348 334 311 295 282 271 263

100 1150 741 586 502 448 411 383 361 344 330 307 291 278 268 259 120 1138 732 578 495 442 404 377 355 338 324 302 285 272 262 253 150 1127 724 571 488 435 398 371 349 332 318 296 280 267 256 248

200 1115 715 563 481 429 392 365 343 326 312 290 274 261 251 242 250 1109 710 559 477 425 388 361 340 323 309 287 271 258 248 239 300 1104 707 556 475 422 386 359 338 321 307 285 269 256 246 237 400 1099 703 553 471 419 383 356 335 318 304 282 266 253 243 234 500 1096 700 551 469 418 381 354 333 316 302 281 264 252 241 233

600 1094 699 549 468 416 380 353 332 315 301 280 263 251 240 232 750 1091 697 548 467 415 379 352 331 314 300 278 262 249 239 231

1000 1089 696 546 465 414 378 351 330 313 299 277 261 248 238 230

5

STATISTICAL TABLES ~ middottt t

TABLE A3 (continued)

F Distribution Critical Values of F (1 significance level)

VI 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 12

1 405218 499950 540335 562458 576365 585899 592836 598107 602247 605585 610632 614267 617010 619153 620873

2 9850 9900 9917 9925 9930 9933 9936 9937 9939 9940 9942 9943 9944 9944 9945 3 3412 3082 2946 2871 2824 2791 2767 2749 2735 2723 2705 2692 2683 2675 2669 4 2120 1800 1669 1598 1552 1521 1498 1480 1466 1455 1437 1425 1415 1408 1402 5 1626 1327 1206 1139 1097 1067 1046 1029 1016 1005 989 977 968 961 955

6 1375 1092 978 915 875 847 826 810 798 787 772 760 752 745 740 7 1225 955 845 785 746 719 699 684 672 662 647 636 628 621 616 8 1126 865 759 701 663 637 618 603 591 581 567 556 548 541 536 9 1056 802 699 642 606 580 561 547 535 526 511 501 492 486 481

10 1004 756 655 599 564 539 520 506 494 485 471 460 452 446 441

11 965 721 622 567 532 507 489 474 463 454 440 429 421 415 410 12 933 693 595 541 506 482 464 450 439 430 416 405 397 391 386 13 907 670 574 521 486 462 444 430 419 410 396 386 378 372 366 14 886 651 556 504 469 446 428 414 403 394 380 370 362 356 351 15 868 636 542 489 456 432 414 400 389 380 367 356 349 342 337

16 853 623 529 477 444 420 403 389 378 369 355 345 337 331 326 17 840 611 518 467 434 410 393 379 368 359 346 335 327 321 316 18 829 601 509 458 425 401 384 371 360 351 337 327 319 313 308 19 818 593 501 450 417 394 377 363 352 343 330 319 312 305 300 20 810 585 494 443 410 387 370 356 346 337 323 313 305 299 294

21 802 578 487 437 404 381 364 351 340 331 317 307 299 293 288 22 795 572 482 431 399 376 359 345 335 326 312 302 294 288 283 23 788 566 476 426 394 371 354 341 330 321 307 297 289 283 278 24 782 561 472 422 390 367 350 336 326 317 303 293 285 279 274 25 777 557 468 418 385 363 346 332 322 313 299 289 281 275 270

26 772 553 464 414 382 359 342 329 318 309 296 286 278 272 266 27 768 549 460 411 378 356 339 326 315 306 293 282 275 268 263 28 764 545 457 407 375 353 336 323 312 303 290 279 272 265 260 29 760 542 454 404 373 350 333 320 309 300 287 277 269 263 257 30 756 539 451 402 370 347 330 317 307 298 284 274 266 260 255

35 742 527 440 391 359 337 320 307 296 288 274 264 256 250 244 40 731 518 431 383 351 329 312 299 289 280 266 256 248 242 237 50 717 506 420 372 341 319 302 289 278 270 256 246 238 232 227 60 708 498 413 365 334 312 295 282 272 263 250 239 231 225 220 70 701 492 407 360 329 307 291 278 267 259 245 235 227 220 215

80 696 488 404 356 326 304 287 274 264 255 242 231 223 217 212 90 693 485 401 353 323 301 284 272 261 252 239 229 221 214 209

100 690 482 398 351 321 299 282 269 259 250 237 227 219 212 207 120 685 479 395 348 317 296 279 266 256 247 234 223 215 209 203 150 681 475 391 345 314 292 276 263 253 244 231 220 212 206 200

200 676 471 388 341 311 289 273 260 250 241 227 217 209 203 197 250 674 469 386 340 309 287 271 258 248 239 226 215 207 201 195 300 672 468 385 338 308 286 270 257 247 238 224 214 206 199 194 400 670 466 383 337 306 285 268 256 245 237 223 213 205 198 192 500 669 465 382 336 305 284 268 255 244 236 222 212 204 197 192

600 668 464 381 335 305 283 267 254 244 235 221 211 203 196 191 750 667 463 381 334 304 283 266 253 243 234 221 211 202 196 190

1000 666 463 380 334 304 282 266 253 243 234 220 210 202 195 190

STATISTICAL TABLES

d litimiddot 6

TABLE A3 (continued)

F Distribution Critical Values of F (1 significance level)

Vi 25 30 35 40 50 60 75 100 150 200 V2

1 623983 626065 627557 628678 630252 631303 632356 633411 634468 634997 2 9946 9947 9947 9947 9948 9948 9949 9949 9949 9949 3 2658 2650 2645 2641 2635 2632 2628 2624 2620 2618 4 1391 1384 1379 1375 1369 1365 1361 1358 1354 1352 5 945 938 933 929 924 920 917 913 909 908

6 730 723 718 714 709 706 702 699 695 693 7 606 599 594 591 586 582 579 575 572 570 8 526 520 515 512 507 503 500 496 493 491 9 471 465 460 457 452 448 445 441 438 436

10 431 425 420 417 412 408 405 401 398 396

11 401 394 389 386 381 378 374 371 367 366 12 376 370 365 362 357 354 350 347 343 341 13 357 351 346 343 338 334 331 327 324 322 14 341 335 330 327 322 318 315 311 308 306 15 328 321 317 313 308 305 301 298 294 292

16 316 310 305 302 297 293 290 286 283 281 17 307 300 296 292 287 283 280 276 273 271 18 298 292 287 284 278 275 271 268 264 262 19 291 284 280 276 271 267 264 260 257 255 20 284 278 273 269 264 261 257 254 250 248

21 279 272 267 264 258 255 251 248 244 242 22 273 267 262 258 253 250 246 242 238 236 23 269 262 257 254 248 245 241 237 234 232 24 264 258 253 249 244 240 237 233 229 227 25 260 254 249 245 240 236 233 229 225 223

26 257 250 245 242 236 233 229 225 221 219 27 254 247 242 238 233 229 226 222 218 216 28 251 244 239 235 230 226 223 219 215 213 29 248 241 236 233 227 223 220 216 212 210 30 245 239 234 230 225 221 217 213 209 207

35 235 228 223 219 214 210 206 202 198 196 40 227 220 215 211 206 202 198 194 190 187 50 217 210 205 201 195 191 187 182 178 176 60 210 203 198 194 188 184 179 175 170 168 70 205 198 193 189 183 178 174 170 165 162

80 201 194 189 185 179 175 170 165 161 158 90 199 192 186 182 176 172 167 162 157 155

100 197 189 184 180 174 169 165 160 155 152 120 193 186 181 176 170 166 161 156 151 148 150 190 183 177 173 166 162 157 152 146 143

200 187 179 174 169 163 158 153 148 142 139 250 185 177 172 167 161 156 151 146 140 136 300 184 176 170 166 159 155 150 144 138 135 400 182 175 169 164 158 153 148 142 136 132 500 181 174 i68 163 157 152 147 141 134 131

600 180 173 167 163 156 151 146 140 134 130 750 180 172 166 162 155 150 145 139 133 129

1000 179 172 166 161 154 150 144 138 132 128

middot STATISTICAL TABLES 7 -t11

TABLE A3 (continued)

F Distribution Critical Values of F(O1 significance level)

VI 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 Vz

1 405e05 500e05 540005 562005 576e05 586e05 593e05 598e05 602e05 606e05 611005 614e05 617e05 619005 621e05

2 99850 99900 99917 99925 99930 99933 99936 99937 99939 99940 99942 99943 99944 99944 99945 3 16703 14850 14111 13710 13458 13285 13158 13062 12986 12925 12832 12764 12714 12674 12642 4 7414 6125 5618 5344 5171 5053 4966 4900 4847 4805 4741 4695 4660 4632 4610 5 47183712 3320 3109 2975 2883 2816 2765 2724 2692 2642 2606 2578 2557 2539

6 3551 2700 2370 2192 2080 2003 1946 1903 1869 1841 1799 1768 1745 1727 1712 7 2925 2169 1877 1720 1621 1552 1502 1463 1433 1408 1371 1343 1323 1306 1293 8 2541 1849 1583 1439 1348 1286 1240 1205 1177 1154 1119 1094 1075 1060 1048 9 2286 1639 1390 1256 1171 1113 1070 1037 1011 989 957 933 915 901 890

10 2104 1491 1255 1128 1048 993 952 920 896 875 845 822 805 791 780

11 1969 1381 1156 1035 958 905 866 835 812 792 763 741 724 711 701 12 1864 1297 1080 963 889 838 800 771 748 729 700 679 663 651 640 13 1782 1231 1021 907 835 786 749 721 698 680 652 631 616 603 593 14 1714 1178 973 862 792 744 708 680 658 640 613 593 578 566 556 15 1659 1134 934 825 757 709 674 647 626 608 581 562 546 535 525

16 1612 1097 901 794 727 680 646 619 598 581 555 535 520 509 499 17 1572 1066 873 768 702 656 622 596 575 558 532 513 499 487 478 18 1538 1039 849 746 681 635 602 576 556 539 513 494 480 468 459 19 1508 1016 828 127 662 618 585 559 539 522 497 478 464 452 443 20 1482 995 810 710 646 602 569 544 524 508 482 464 449 438 429

21 1459 977 794 695 632 588 556 531 511 495 470 451 437 426 417 22 1438 961 780 681 619 576 544 519 499 483 458 440 426 415 406 23 1420 947 767 670 608 565 533 509 489 473 448 430 416 405 396 24 1403 934 755 659 598 555 523 499 480 464 439 421 407 396 387 25 1388 922 745 649 589 546 515 491 471 456 431 413 399 388 379

26 1374 912 736 641 580 538 507 483 464 448 424 406 392 381 372 27 1361 902 727 633 573 531 500 476 457 441 417 399 386 375 366 28 1350 893 719 625 566 524 493 469 450 435 411 393 380 369 360 29 1339 885 712 619 559 518 487 464 445 429 405 388 374 363 354 30 1329 877 705 612 553 512 482 458 439 424 400 382 369 358 349

35 1290 847 679 588 530 489 459 436 418 403 379 362 348 338 329 40 1261 825 659 570 513 473 444 421 402 387 364 347 334 323 314 50 1222 796 634 546 490 451 422 400 382 367 344 327 341 304 295 60 1197 777 617 531 476 437 409 386 369 354 332 315 302 291 283 70 1180 764 606 520 466 428 399 377 360 345 323 306 293 283 274

80 1167 754 597 512 458 420 392 370 353 339 316 300 287 276 268 90 1157 747 591 506 453 415 387 365 348 334 311 295 282 271 263

100 1150 741 586 502 448 411 383 361 344 330 307 291 278 268 259 120 1138 732 578 495 442 404 377 355 338 324 302 285 272 262 253 150 1127 724 571 488 435 398 371 349 332 318 296 280 267 256 248

200 1115 715 563 481 429 392 365 343 326 312 290 274 261 251 242 250 1109 710 559 477 425 388 361 340 323 309 287 271 258 248 239 300 1104 707 556 475 422 386 359 338 321 307 285 269 256 246 237 400 1099 703 553 471 419 383 356 335 318 304 282 266 253 243 234 500 1096 700 551 469 418 381 354 333 316 302 281 264 252 241 233

600 1094 699 549 468 416 380 353 332 315 301 280 263 251 240 232 750 1091 697 548 467 415 379 352 331 314 300 278 262 249 239 231

1000 1089 696 546 465 414 378 351 330 313 299 277 261 248 238 230

STATISTICAL TABLES

d litimiddot 6

TABLE A3 (continued)

F Distribution Critical Values of F (1 significance level)

Vi 25 30 35 40 50 60 75 100 150 200 V2

1 623983 626065 627557 628678 630252 631303 632356 633411 634468 634997 2 9946 9947 9947 9947 9948 9948 9949 9949 9949 9949 3 2658 2650 2645 2641 2635 2632 2628 2624 2620 2618 4 1391 1384 1379 1375 1369 1365 1361 1358 1354 1352 5 945 938 933 929 924 920 917 913 909 908

6 730 723 718 714 709 706 702 699 695 693 7 606 599 594 591 586 582 579 575 572 570 8 526 520 515 512 507 503 500 496 493 491 9 471 465 460 457 452 448 445 441 438 436

10 431 425 420 417 412 408 405 401 398 396

11 401 394 389 386 381 378 374 371 367 366 12 376 370 365 362 357 354 350 347 343 341 13 357 351 346 343 338 334 331 327 324 322 14 341 335 330 327 322 318 315 311 308 306 15 328 321 317 313 308 305 301 298 294 292

16 316 310 305 302 297 293 290 286 283 281 17 307 300 296 292 287 283 280 276 273 271 18 298 292 287 284 278 275 271 268 264 262 19 291 284 280 276 271 267 264 260 257 255 20 284 278 273 269 264 261 257 254 250 248

21 279 272 267 264 258 255 251 248 244 242 22 273 267 262 258 253 250 246 242 238 236 23 269 262 257 254 248 245 241 237 234 232 24 264 258 253 249 244 240 237 233 229 227 25 260 254 249 245 240 236 233 229 225 223

26 257 250 245 242 236 233 229 225 221 219 27 254 247 242 238 233 229 226 222 218 216 28 251 244 239 235 230 226 223 219 215 213 29 248 241 236 233 227 223 220 216 212 210 30 245 239 234 230 225 221 217 213 209 207

35 235 228 223 219 214 210 206 202 198 196 40 227 220 215 211 206 202 198 194 190 187 50 217 210 205 201 195 191 187 182 178 176 60 210 203 198 194 188 184 179 175 170 168 70 205 198 193 189 183 178 174 170 165 162

80 201 194 189 185 179 175 170 165 161 158 90 199 192 186 182 176 172 167 162 157 155

100 197 189 184 180 174 169 165 160 155 152 120 193 186 181 176 170 166 161 156 151 148 150 190 183 177 173 166 162 157 152 146 143

200 187 179 174 169 163 158 153 148 142 139 250 185 177 172 167 161 156 151 146 140 136 300 184 176 170 166 159 155 150 144 138 135 400 182 175 169 164 158 153 148 142 136 132 500 181 174 i68 163 157 152 147 141 134 131

600 180 173 167 163 156 151 146 140 134 130 750 180 172 166 162 155 150 145 139 133 129

1000 179 172 166 161 154 150 144 138 132 128

middot STATISTICAL TABLES 7 -t11

TABLE A3 (continued)

F Distribution Critical Values of F(O1 significance level)

VI 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 Vz

1 405e05 500e05 540005 562005 576e05 586e05 593e05 598e05 602e05 606e05 611005 614e05 617e05 619005 621e05

2 99850 99900 99917 99925 99930 99933 99936 99937 99939 99940 99942 99943 99944 99944 99945 3 16703 14850 14111 13710 13458 13285 13158 13062 12986 12925 12832 12764 12714 12674 12642 4 7414 6125 5618 5344 5171 5053 4966 4900 4847 4805 4741 4695 4660 4632 4610 5 47183712 3320 3109 2975 2883 2816 2765 2724 2692 2642 2606 2578 2557 2539

6 3551 2700 2370 2192 2080 2003 1946 1903 1869 1841 1799 1768 1745 1727 1712 7 2925 2169 1877 1720 1621 1552 1502 1463 1433 1408 1371 1343 1323 1306 1293 8 2541 1849 1583 1439 1348 1286 1240 1205 1177 1154 1119 1094 1075 1060 1048 9 2286 1639 1390 1256 1171 1113 1070 1037 1011 989 957 933 915 901 890

10 2104 1491 1255 1128 1048 993 952 920 896 875 845 822 805 791 780

11 1969 1381 1156 1035 958 905 866 835 812 792 763 741 724 711 701 12 1864 1297 1080 963 889 838 800 771 748 729 700 679 663 651 640 13 1782 1231 1021 907 835 786 749 721 698 680 652 631 616 603 593 14 1714 1178 973 862 792 744 708 680 658 640 613 593 578 566 556 15 1659 1134 934 825 757 709 674 647 626 608 581 562 546 535 525

16 1612 1097 901 794 727 680 646 619 598 581 555 535 520 509 499 17 1572 1066 873 768 702 656 622 596 575 558 532 513 499 487 478 18 1538 1039 849 746 681 635 602 576 556 539 513 494 480 468 459 19 1508 1016 828 127 662 618 585 559 539 522 497 478 464 452 443 20 1482 995 810 710 646 602 569 544 524 508 482 464 449 438 429

21 1459 977 794 695 632 588 556 531 511 495 470 451 437 426 417 22 1438 961 780 681 619 576 544 519 499 483 458 440 426 415 406 23 1420 947 767 670 608 565 533 509 489 473 448 430 416 405 396 24 1403 934 755 659 598 555 523 499 480 464 439 421 407 396 387 25 1388 922 745 649 589 546 515 491 471 456 431 413 399 388 379

26 1374 912 736 641 580 538 507 483 464 448 424 406 392 381 372 27 1361 902 727 633 573 531 500 476 457 441 417 399 386 375 366 28 1350 893 719 625 566 524 493 469 450 435 411 393 380 369 360 29 1339 885 712 619 559 518 487 464 445 429 405 388 374 363 354 30 1329 877 705 612 553 512 482 458 439 424 400 382 369 358 349

35 1290 847 679 588 530 489 459 436 418 403 379 362 348 338 329 40 1261 825 659 570 513 473 444 421 402 387 364 347 334 323 314 50 1222 796 634 546 490 451 422 400 382 367 344 327 341 304 295 60 1197 777 617 531 476 437 409 386 369 354 332 315 302 291 283 70 1180 764 606 520 466 428 399 377 360 345 323 306 293 283 274

80 1167 754 597 512 458 420 392 370 353 339 316 300 287 276 268 90 1157 747 591 506 453 415 387 365 348 334 311 295 282 271 263

100 1150 741 586 502 448 411 383 361 344 330 307 291 278 268 259 120 1138 732 578 495 442 404 377 355 338 324 302 285 272 262 253 150 1127 724 571 488 435 398 371 349 332 318 296 280 267 256 248

200 1115 715 563 481 429 392 365 343 326 312 290 274 261 251 242 250 1109 710 559 477 425 388 361 340 323 309 287 271 258 248 239 300 1104 707 556 475 422 386 359 338 321 307 285 269 256 246 237 400 1099 703 553 471 419 383 356 335 318 304 282 266 253 243 234 500 1096 700 551 469 418 381 354 333 316 302 281 264 252 241 233

600 1094 699 549 468 416 380 353 332 315 301 280 263 251 240 232 750 1091 697 548 467 415 379 352 331 314 300 278 262 249 239 231

1000 1089 696 546 465 414 378 351 330 313 299 277 261 248 238 230

middot STATISTICAL TABLES 7 -t11

TABLE A3 (continued)

F Distribution Critical Values of F(O1 significance level)

VI 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 Vz

1 405e05 500e05 540005 562005 576e05 586e05 593e05 598e05 602e05 606e05 611005 614e05 617e05 619005 621e05

2 99850 99900 99917 99925 99930 99933 99936 99937 99939 99940 99942 99943 99944 99944 99945 3 16703 14850 14111 13710 13458 13285 13158 13062 12986 12925 12832 12764 12714 12674 12642 4 7414 6125 5618 5344 5171 5053 4966 4900 4847 4805 4741 4695 4660 4632 4610 5 47183712 3320 3109 2975 2883 2816 2765 2724 2692 2642 2606 2578 2557 2539

6 3551 2700 2370 2192 2080 2003 1946 1903 1869 1841 1799 1768 1745 1727 1712 7 2925 2169 1877 1720 1621 1552 1502 1463 1433 1408 1371 1343 1323 1306 1293 8 2541 1849 1583 1439 1348 1286 1240 1205 1177 1154 1119 1094 1075 1060 1048 9 2286 1639 1390 1256 1171 1113 1070 1037 1011 989 957 933 915 901 890

10 2104 1491 1255 1128 1048 993 952 920 896 875 845 822 805 791 780

11 1969 1381 1156 1035 958 905 866 835 812 792 763 741 724 711 701 12 1864 1297 1080 963 889 838 800 771 748 729 700 679 663 651 640 13 1782 1231 1021 907 835 786 749 721 698 680 652 631 616 603 593 14 1714 1178 973 862 792 744 708 680 658 640 613 593 578 566 556 15 1659 1134 934 825 757 709 674 647 626 608 581 562 546 535 525

16 1612 1097 901 794 727 680 646 619 598 581 555 535 520 509 499 17 1572 1066 873 768 702 656 622 596 575 558 532 513 499 487 478 18 1538 1039 849 746 681 635 602 576 556 539 513 494 480 468 459 19 1508 1016 828 127 662 618 585 559 539 522 497 478 464 452 443 20 1482 995 810 710 646 602 569 544 524 508 482 464 449 438 429

21 1459 977 794 695 632 588 556 531 511 495 470 451 437 426 417 22 1438 961 780 681 619 576 544 519 499 483 458 440 426 415 406 23 1420 947 767 670 608 565 533 509 489 473 448 430 416 405 396 24 1403 934 755 659 598 555 523 499 480 464 439 421 407 396 387 25 1388 922 745 649 589 546 515 491 471 456 431 413 399 388 379

26 1374 912 736 641 580 538 507 483 464 448 424 406 392 381 372 27 1361 902 727 633 573 531 500 476 457 441 417 399 386 375 366 28 1350 893 719 625 566 524 493 469 450 435 411 393 380 369 360 29 1339 885 712 619 559 518 487 464 445 429 405 388 374 363 354 30 1329 877 705 612 553 512 482 458 439 424 400 382 369 358 349

35 1290 847 679 588 530 489 459 436 418 403 379 362 348 338 329 40 1261 825 659 570 513 473 444 421 402 387 364 347 334 323 314 50 1222 796 634 546 490 451 422 400 382 367 344 327 341 304 295 60 1197 777 617 531 476 437 409 386 369 354 332 315 302 291 283 70 1180 764 606 520 466 428 399 377 360 345 323 306 293 283 274

80 1167 754 597 512 458 420 392 370 353 339 316 300 287 276 268 90 1157 747 591 506 453 415 387 365 348 334 311 295 282 271 263

100 1150 741 586 502 448 411 383 361 344 330 307 291 278 268 259 120 1138 732 578 495 442 404 377 355 338 324 302 285 272 262 253 150 1127 724 571 488 435 398 371 349 332 318 296 280 267 256 248

200 1115 715 563 481 429 392 365 343 326 312 290 274 261 251 242 250 1109 710 559 477 425 388 361 340 323 309 287 271 258 248 239 300 1104 707 556 475 422 386 359 338 321 307 285 269 256 246 237 400 1099 703 553 471 419 383 356 335 318 304 282 266 253 243 234 500 1096 700 551 469 418 381 354 333 316 302 281 264 252 241 233

600 1094 699 549 468 416 380 353 332 315 301 280 263 251 240 232 750 1091 697 548 467 415 379 352 331 314 300 278 262 249 239 231

1000 1089 696 546 465 414 378 351 330 313 299 277 261 248 238 230

STATISTICAL TABLES c

8 ~

TABLE Aa (continued)

F Distribution Critical Values of F (01 significance level)

VI 25 30 35 40 50 60 75 100 150 200 Vz

1 624005 6lt26005 628005 62ge05 630e05 6lt31e05 632e05 633005 635e05 635005

2 99946 99947 99947 99947 99948 99948 99949 99949 99949 99949 3 12584 12545 12517 12496 12466 12447 12427 124Q7 12387 12377 4 4570 4543 4523 4509 4488 4475 4461 4447 4433 4426 5 2508 2487 2472 2460 2444 2433 2412 2412 2401 2395

lt

6 7 8 9

10

1685 1269 1026 869 760

1667 1253 1011 855 747

1654 1241 1000 846 737

1644 1233 992 837 730

1631 1220 980 826 719

1621 1212 973 819 712

1612 1204 965 811 705

1603 1195 957 804 698

1593 1187 949 796 691

1589 1182 945 793 687

11 12 13 14 15

681 622 575 538 507

668 609 563 525 495

659 600 554 517 486

652 593

547 510 480

642 583 537 500 470

635 576 530 494 464

628 570 524 487 457

621 563 517 481 451

614 556 510 474 444

610 552 507 471 441

16 17 18 19 20

482 460 442 426 412

470 448 430 414 400

461 440 422 406 392

454 433 415 399 386

445 424 406 390 377

439 418 400 384 370

432 411 393 378 364

426 405 387 371 358

419 398 380 365 351

416 395 377 361 348

21 22 23 24 25

400 389 379 371 363

388 378 368 359 352

380 370 360 351 343

374 363 353 345 337

364 354 344 336 328

358 348 338 329 322

352 341 332 323 315

346 335 325 317 309

339 328 319 310 303

336 325 316 307 299

26 27 28 29 30

356 349 343 338 333

344 338 332 327 322

336 330 324 318 313

330 323 318 312 307

321 314 309 303 298

315 308 302 297 292

308 302 296 291 286

302 296 290 284 279

295 289 283 278 273

292 286 280 274 269

35 40 50 60 70

313 298 279 267 258

302 287 268 255 247

293 279 260 247 239

287 273 253 241 232

278 264 244 232 223

272 257 238 225 216

266 251 231 219 210

259 244 225 212 203

252 238 218 205 195

249 234 214 201 192

80 90

100 120 150

252 247 243 237 232

241 236 232 226 221

232 227 224 218 212

226 221 217 211 206

216 211 208 202 196

210 205 201 195 189

203 198 194 188 182

196 191 187 l81 174

189 183 179 173 166

185 179 175 168 1~62

200 250 300 400 500

226 223 221 218 217

215 212 210 207 205

207 203 201 198 197

200 197 194 192 190

190 187 185 182 180

183 180 178 175 173

176 172 170 167 165

168 165 162 159 157

160 156 153 150 148

155 151 148 145 143

600 750

1000

216 215 214

204 203 202

196 195 194

189 188 187

179 178 177

172 171 169

l64 163 162

156 155 153

146 145 144

141 140 138

5

10

15

20

25

30

Chi-Square Distribution Table

The shaded area is equal to ex for X2 X~

I I

I

I

I

i I

1 j 0000

I 0000 0001 0004 0016 2706 3841 5024 6635 7879

2 0010 0020 0051 0103 021l 4605 5991 7378 9210 10597 3 0072 0115 0216 0352 0584 6251 7815 9348 1l345 12838 4 0207 0297 0484 071l 1064 7779 9488 1l143

I 13277 14860

0412 0554 0831 1145 1610 9236 11070 12833 15086 16750 6 0676 0872 1237 1635 2204 10645 12592 14449 16812 18548 7 0989 1239 1690 2167 2833 12017 14067 16013 18475 20278 8 1344 1646 2180 2733 3490 13362 15507 17535 20090 21955 9 1735 2088 2700 3325 4168 14684 16919 19023 21666 23589

1

2156 2558 3247 3940 4865 15987 18307 I 20483 23209 25188

111 2603 3053 3816 4575 5578

I 17275 19675 21920 24725 26757

12 3074 3571 4404 5226 6304 18549 21026 2a337 26217 28300 13 middot3565 4107 5009 5892 i 7042 19812 22362 24736 27688 29819 14 4075 4660 5629 6571 7790 21064 23685 261l9 291lt11 31319

4601 5229 6262 I 7261 8547 22307 24996 27488 30578 32801 16 5142 5812 6908 7962 9312 23542 26296 28845 32000 34267 17 5697 6408 Y564 8672 10085 24769 27587 30191 33409 35718 18 6265 7015 8231 9390 10865 25989 28869 31526 34805 37156

I19 6844 7633 8907 101l7 1l651 27~204 30144 32852 36191 38582

7434 8260 9591 10851 12443 28412 31410 34170 37566 39997 21 8034 I 8897 10283 11591 13240 29615 1 32671 35479 38932

I 41401

22 8643 9542 10982 12338 14041 30813 33924 36781 40289 42796 23 9260 10196 11689 13091 14848 32007 35172 38076 41638 44181 24 9886 10856 12401 13848 15659 33196 36415 39364 42980 45559

i 10520 11524 13120 1461l 16473 34382 37652 40646 44314 46928 i 26 11160 12198 I 13844

I 15379 17292 I 35563 38885 41923 45642 48290 I

27 11808 12879 14573 16151 18114 36741 40113 43195 46963 49645 28 12461 13565 15308 16928 18939 37916 41337 44461 48278 50993 bull 29 13121 14256 16047 17708 19768 39087 42557 45722 49588 52336

13787 14953 16791 18493 20599 40256 43773 46979 50892 53672 40 20707 I 22164 24433 26509 29051 51805 I 55758 59342 63691 66766 50 27991 29707 32357 34764 37689 63167 bull 67505 71420 76154 79490 60 35534 bull 37485 40482 43188 I 46459 74397 79082 83298 i 88379 91952 70 43275 45442 48758 51 739 55329 85527 90531 95023 100425 104215middot 80 51172 53540 57153 I 60391 I 64278 96578 101879 106629 I 1123291 1l6321 90 59196 61754 65647 69126 I 73291 107565 11l3145 1l8136 124116 128299 100 67328 70065 74 222 77929 82358 1l8498 124342 129561 135807 i 140169

5

10

15

20

25

30

Chi-Square Distribution Table

The shaded area is equal to ex for X2 X~

I I

I

I

I

i I

1 j 0000

I 0000 0001 0004 0016 2706 3841 5024 6635 7879

2 0010 0020 0051 0103 021l 4605 5991 7378 9210 10597 3 0072 0115 0216 0352 0584 6251 7815 9348 1l345 12838 4 0207 0297 0484 071l 1064 7779 9488 1l143

I 13277 14860

0412 0554 0831 1145 1610 9236 11070 12833 15086 16750 6 0676 0872 1237 1635 2204 10645 12592 14449 16812 18548 7 0989 1239 1690 2167 2833 12017 14067 16013 18475 20278 8 1344 1646 2180 2733 3490 13362 15507 17535 20090 21955 9 1735 2088 2700 3325 4168 14684 16919 19023 21666 23589

1

2156 2558 3247 3940 4865 15987 18307 I 20483 23209 25188

111 2603 3053 3816 4575 5578

I 17275 19675 21920 24725 26757

12 3074 3571 4404 5226 6304 18549 21026 2a337 26217 28300 13 middot3565 4107 5009 5892 i 7042 19812 22362 24736 27688 29819 14 4075 4660 5629 6571 7790 21064 23685 261l9 291lt11 31319

4601 5229 6262 I 7261 8547 22307 24996 27488 30578 32801 16 5142 5812 6908 7962 9312 23542 26296 28845 32000 34267 17 5697 6408 Y564 8672 10085 24769 27587 30191 33409 35718 18 6265 7015 8231 9390 10865 25989 28869 31526 34805 37156

I19 6844 7633 8907 101l7 1l651 27~204 30144 32852 36191 38582

7434 8260 9591 10851 12443 28412 31410 34170 37566 39997 21 8034 I 8897 10283 11591 13240 29615 1 32671 35479 38932

I 41401

22 8643 9542 10982 12338 14041 30813 33924 36781 40289 42796 23 9260 10196 11689 13091 14848 32007 35172 38076 41638 44181 24 9886 10856 12401 13848 15659 33196 36415 39364 42980 45559

i 10520 11524 13120 1461l 16473 34382 37652 40646 44314 46928 i 26 11160 12198 I 13844

I 15379 17292 I 35563 38885 41923 45642 48290 I

27 11808 12879 14573 16151 18114 36741 40113 43195 46963 49645 28 12461 13565 15308 16928 18939 37916 41337 44461 48278 50993 bull 29 13121 14256 16047 17708 19768 39087 42557 45722 49588 52336

13787 14953 16791 18493 20599 40256 43773 46979 50892 53672 40 20707 I 22164 24433 26509 29051 51805 I 55758 59342 63691 66766 50 27991 29707 32357 34764 37689 63167 bull 67505 71420 76154 79490 60 35534 bull 37485 40482 43188 I 46459 74397 79082 83298 i 88379 91952 70 43275 45442 48758 51 739 55329 85527 90531 95023 100425 104215middot 80 51172 53540 57153 I 60391 I 64278 96578 101879 106629 I 1123291 1l6321 90 59196 61754 65647 69126 I 73291 107565 11l3145 1l8136 124116 128299 100 67328 70065 74 222 77929 82358 1l8498 124342 129561 135807 i 140169