Appendix C. Tables 5,040 40, ,880 3,628,800

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1 Appendix C Tables Table A Factorials Table B The Binomial Distribution Table C The Poisson Distribution n n! Table D Random Numbers 0 1 Table E The Standard Normal Distribution 1 1 Table F The t Distribution 2 2 Table G The Chi-Square Distribution 3 6 Table H The F Distribution 4 24 Table I Critical Values for the PPMC Table J Critical Values for the Sign Test Table K Critical Values for the Wilcoxon Signed-Rank Test Table Critical Values for the Rank Correlation Coefficient Table M Critical Values for the Number of Runs Table N Critical Values for the Tukey Test Table A Factorials , , , ,628, ,916, ,001, ,227,020, ,178,291, ,307,674,368, ,922,789,888, ,687,428,096, ,402,373,705,728, ,645,100,408,832, ,432,902,008,176,640,000 A 17

2 770 Appendix C Tables Table B The Binomial Distribution n x p A 18

3 Appendix C Tables 771 Table B (continued) n x p A 19

4 772 Appendix C Tables Table B (continued) n x p A 20

5 Appendix C Tables 773 Table B (continued) n x p A 21

6 774 Appendix C Tables Table B (continued) n x p A 22

7 Appendix C Tables 775 Table B (concluded) n x Note: All values of or less are omitted. Source: J. Freund and G. Simon, Modern Elementary Statistics, Table The Binomial Distribution, 1992 Prentice-Hall, Inc. Reproduced by permission of Pearson Education, Inc. p A 23

8 768 Appendix B 3 Alternate Approach to the Standard Normal Distribution Table B 1 The Standard Normal Distribution z For z values greater than 3.49, use Area given in table 0 z A 16

9 776 Appendix C Tables Table C The Poisson Distribution x x x x A 24

10 Appendix C Tables 777 Table C (continued) x x x A 25

11 778 Appendix C Tables Table C (continued) x x A 26

12 Appendix C Tables 779 Table C (continued) x x A 27

13 780 Appendix C Tables Table C (continued) x x A 28

14 Appendix C Tables 781 Table C (continued) x x A 29

15 782 Appendix C Tables Table C (concluded) x Reprinted with permission from W. H. Beyer, Handbook of Tables for Probability and Statistics, 2nd ed. Copyright CRC Press, Boca Raton, Fla., A 30

16 Appendix C Tables 783 Table D Random Numbers Reprinted with permission from W. H. Beyer, Handbook of Tables for Probability and Statistics, 2nd ed. Copyright CRC Press, Boca Raton, Fla., A 31

17 784 Appendix C Tables Table E The Standard Normal Distribution Cumulative Standard Normal Distribution z For z values less than 3.49, use Area z 0 A 32

18 Appendix C Tables 785 Table E (continued) Cumulative Standard Normal Distribution z For z values greater than 3.49, use Area 0 z A 33

19 786 Appendix C Tables Table F The t Distribution Confidence intervals 80% 90% 95% 98% 99% One tail, A d.f. Two tails, A (z) a b c d a This value has been rounded to 1.28 in the textbook. b This value has been rounded to 1.65 in the textbook. c This value has been rounded to 2.33 in the textbook. d This value has been rounded to 2.58 in the textbook. Source: Adapted from W. H. Beyer, Handbook of Tables for Probability and Statistics, 2nd ed., CRC Press, Boca Raton, Fla., Reprinted with permission. One tail t Area Two tails Area Area 2 2 t t A 34

20 Appendix C Tables 787 Table G The Chi-Square Distribution Degrees of A freedom Source: Owen, Handbook of Statistical Tables, Table A 4 Chi-Square Distribution Table, 1962 by Addison-Wesley Publishing Company, Inc. Copyright renewal Reproduced by permission of Pearson Education, Inc. Area 2 A 35

21 A 36 Table H The F Distribution A d.f.d.: degrees of d.f.n.: degrees of freedom, numerator freedom, denominator Appendix C Tables 1 16,211 20,000 21,615 22,500 23,056 23,437 23,715 23,925 24,091 24,224 24,426 24,630 24,836 24,940 25,044 25,148 25,253 25,359 25,

22 Table H (continued) A 0.01 d.f.d.: degrees of d.f.n.: degrees of freedom, numerator freedom, denominator A Appendix C Tables 789

23 A 38 Table H (continued) A d.f.d.: degrees of d.f.n.: degrees of freedom, numerator freedom, denominator Appendix C Tables

24 Table H (continued) A 0.05 d.f.d.: degrees of d.f.n.: degrees of freedom, numerator freedom, denominator A Appendix C Tables 791

25 A 40 Table H (concluded) A 0.10 d.f.d.: degrees of d.f.n.: degrees of freedom, numerator freedom, denominator Appendix C Tables From M. Merrington and C. M. Thompson (1943). Table of Percentage Points of the Inverted Beta (F) Distribution. Biometrika 33, pp Reprinted with permission from Biometrika.

26 Appendix C Tables 793 Table I Critical Values for the PPMC Reject H 0 : r 0 if the absolute value of r is greater than the value given in the table. The values are for a two-tailed test; d.f. n 2. d.f. A 0.05 A Table J Critical Values for the Sign Test Reject the null hypothesis if the smaller number of positive or negative signs is less than or equal to the value in the table. One-tailed, A A 0.01 A A 0.05 Two-tailed, n A 0.01 A 0.02 A 0.05 A Note: Table J is for one-tailed or two-tailed tests. The term n represents the total number of positive and negative signs. The test value is the number of less frequent signs. Source: Table 1, p. 560, from The Statistical Sign Test by W. J. Dixon and A. M. Mood, vol. 41. no. 236 (Dec. 1946), pp Source: From Biometrika Tables for Statisticians, vol. 1 (1962), p Reprinted with permission. A 41

27 794 Appendix C Tables Table K Critical Values for the Wilcoxon Signed-Rank Test Reject the null hypothesis if the test value is less than or equal to the value given in the table. One-tailed, A 0.05 A A 0.01 A Two-tailed, n A 0.10 A 0.05 A 0.02 A Table Critical Values for the Rank Correlation Coefficient Reject H 0 : r 0 if the absolute value of r S is greater than the value given in the table. n A 0.10 A 0.05 A 0.02 A Source: From N.. Johnson and F. C. eone, Statistical and Experimental Design, vol. I (1964), p Reprinted with permission from the Institute of Mathematical Statistics. Source: From Some Rapid Approximate Statistical Procedures, Copyright 1949, 1964 erderle aboratories, American Cyanamid Co., Wayne, N.J. Reprinted with permission. A 42

28 Appendix C Tables 795 Table M Critical Values for the Number of Runs This table gives the critical values at a 0.05 for a two-tailed test. Reject the null hypothesis if the number of runs is less than or equal to the smaller value or greater than or equal to the larger value. Value of n 2 Value of n Source: Adapted from C. Eisenhardt and F. Swed, Tables for Testing Randomness of Grouping in a Sequence of Alternatives, The Annals of Statistics, vol. 14 (1943), pp Reprinted with permission of the Institute of Mathematical Statistics and of the Benjamin/Cummings Publishing Company, in whose publication, Elementary Statistics, 3rd ed. (1989), by Mario F. Triola, this table appears. A 43

29 A 44 Table N Critical Values for the Tukey Test A 0.01 k v Appendix C Tables

30 A 45 Table N (continued) A 0.05 k v Appendix C Tables 797

31 A 46 Table N (concluded) A 0.10 k v Appendix C Tables Source: Tables of Range and Studentized Range, Annals of Mathematical Statistics, vol. 31, no. 4. Reprinted with permission of the Institute of Mathematical Sciences.

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