Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics

Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical formulae ad tables For first certificatio from Jue 018 for: Advaced Subsidiary GCE i Statistics (8ST0) For first certificatio from Jue 019 for: Advaced GCE i Statistics (9ST0) This copy is the property of Pearso. It is ot to be removed from the eamiatio room or marked i ay way. P58394A 017 Pearso Educatio Ltd. 1/1/1/1/1/1/1/

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Cotets 1 Itroductio 1 AS Level i Statistics 3 A Level i Statistics 4 4 Statistical Tables 8 Table 1: Cumulative Biomial Distributio Fuctio 8 Table : Cumulative Poisso Distributio Fuctio 15 Table 3: Normal Distributio Fuctio 17 Table 4: Percetage Poits of the Normal Distributio 18 Table 5: Percetage Poits of the Studet s t-distributio 19 Table 6: Percetage Poits of the χ Distributio 0 Table 7: Percetage Poits of the F-distributio 1 Table 8: Critical Values of the Product Momet Correlatio Coefficiet 3 Table 9: Critical Values of Spearma s Rak Correlatio Coefficiet 4 Table 10: Critical Values of the Wilcoo Siged-Rak Statistic 5 Table 11: Critical Values of the Wilcoo Rak-Sum 6

1 Itroductio The formulae i this booklet have bee arraged by qualificatio. Studets sittig AS Statistics papers should refer to Sectio, pages 3. Studets sittig A Level Statistics papers should refer to Sectio 3, pages 4 7. Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 1

AS Level i Statistics Populatio variace, σ, = N 1 μ = μ N ( ) Populatio stadard deviatio, σ, = N 1 μ = μ N ( ) Sample variace = 1 1 ( ) = 1 1 ( ) Sample stadard deviatio = 1 1 ( ) = 1 1 ( ) Biomial probability calculatios: P X p ( = ) = 1 p ( ) Mea = p Variace = p(1 p) For a radom sample of observatios from N ( μ, σ ) X μ ~ N(0, 1) σ Test statistic for a biomial proportio usig ormal distributio: pˆ p p ( 1 p) ~ N(0, 1) Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

Product momet correlatio coefficiet: r = S S y S yy = ( ) ( y y) i i { ( y y i ) }{ ( i ) } = i ( ) y i ( i ) y i i i yi ( ) ( y ) i Coefficiets for least squares regressio lie: least squares regressio lie of y o is y = a + b, where a = y b Sy the regressio coefficiet of y o is b = = S Test for associatio: ( O E i i) E i is approimately distributed as χ ( y y i )( i ) ( i ) Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 3

3 A Level i Statistics Populatio variace, σ, = N 1 μ = μ N ( ) Populatio stadard deviatio, σ, = N 1 μ = μ N ( ) Sample variace, s, = 1 1 ( ) = 1 1 ( ) Sample stadard deviatio, s, = 1 1 ( ) = 1 1 ( ) Biomial probability calculatios: P X p ( = ) = 1 p ( ) Biomial mea = p Biomial variace = p (1 p) For a radom sample of observatios from N ( μ, σ ) X μ ~ N(0, 1) σ Test statistic for a biomial proportio usig ormal distributio: pˆ p p ( 1 p) ~ N(0, 1) 4 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

Product momet correlatio coefficiet: r = S S y S yy = ( ) ( y y) i i { ( y y i ) }{ ( i ) } = i ( ) y i ( i ) y i i i yi ( ) ( y ) i Coefficiets for least squares regressio lie: least squares regressio lie of y o is y = a + b, where a = y b Sy the regressio coefficiet of y o is b = = S Bayes theorem for up to three evets: P( A P B A j) ( j) P( A B j ) = P A P B A i= 1 ( i) ( i) ( y y i )( i ) ( i ) The Poisso probability formula: ( = ) = e P X λ λ! Poisso mea = λ Poisso variace = λ The epoetial cumulative probability formula: P(X ) = 1 e λ Epoetial mea = 1 λ 1 Epoetial variace = λ EaX ( ± by) = ae( X) ± be( Y ) ( ) = ( ) + ( ) Var ax ± by a Var X b Var Y, for idepedet variables X ad Y Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 5

For a radom sample of observatios from N (μ, σ ) X μ S ~ t 1 (also valid i matched-pairs situatios) For a radom sample of observatios from N (μ, σ ) ad, idepedetly, a radom sample of y observatios from N (μ y, σ y ) ( X Y) ( μ μ y) σ σ + y y ~ N(0, 1) For a radom sample of observatios from N (μ, σ ) ad, idepedetly, a radom sample of y observatios from N (μ y, σ y ) where σ = σ y = σ (ukow) ( X Y) ( μ μ y) S p = 1 1 S p + ( ) + y 1 S 1 S + ~ t + y where y y y ( ) Test statistic for the differece i two biomial proportios: p p 1 stadard error where stadard error = p p 1 1 ( 1 ) + 1 where p = p + p 1 1 + 1 Test for associatio ad goodess of fit test: ( O E i i) E i is approimately distributed as χ 6 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

Aalysis of variace (oe-way ad two-way): oe-factor model ij = μ + α i + ε ij, where ε ij ~ N (0, σ ) total sum of squares SS T ij i j = T betwee groups sum of squares SS B Ti T = i i two-factor model (with m rows ad colums) ij = μ + α i + β j + ε ij, where ε ij ~ N (0, σ ) total sum of squares SS T ij i j = T m betwee rows sum of squares SS R Ri T = m i betwee colums sum of squares SS C C j T = m m j Cohe s d formula: d = ( 1 ) s where s = ( ) + ( ) 1 s 1 s 1 1 + 1 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 7

4 Statistical Tables Table 1: Cumulative Biomial Distributio Fuctio The tabulated value is P(X ), where X has a biomial distributio with parameters ad p. p 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 0.50 p = 0 0.9801 0.9604 0.9409 0.916 0.905 0.8836 0.8649 0.8464 0.881 0.8100 0.75 0.6400 0.565 0.4900 0.45 0.3600 0.305 0.500 0 1 0.9999 0.9996 0.9991 0.9984 0.9975 0.9964 0.9951 0.9936 0.9919 0.9900 0.9775 0.9600 0.9375 0.9100 0.8775 0.8400 0.7975 0.7500 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 = 3 0 0.9703 0.941 0.917 0.8847 0.8574 0.8306 0.8044 0.7787 0.7536 0.790 0.6141 0.510 0.419 0.3430 0.746 0.160 0.1664 0.150 0 1 0.9997 0.9988 0.9974 0.9953 0.998 0.9896 0.9860 0.9818 0.977 0.970 0.9393 0.8960 0.8438 0.7840 0.7183 0.6480 0.5748 0.5000 1 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9993 0.9990 0.9966 0.990 0.9844 0.9730 0.9571 0.9360 0.9089 0.8750 3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 3 = 4 0 0.9606 0.94 0.8853 0.8493 0.8145 0.7807 0.7481 0.7164 0.6857 0.6561 0.50 0.4096 0.3164 0.401 0.1785 0.196 0.0915 0.065 0 1 0.9994 0.9977 0.9948 0.9909 0.9860 0.9801 0.9733 0.9656 0.9570 0.9477 0.8905 0.819 0.7383 0.6517 0.5630 0.475 0.3910 0.315 1 1.0000 1.0000 0.9999 0.9998 0.9995 0.999 0.9987 0.9981 0.9973 0.9963 0.9880 0.978 0.949 0.9163 0.8735 0.808 0.7585 0.6875 3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9995 0.9984 0.9961 0.9919 0.9850 0.9744 0.9590 0.9375 3 4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 4 = 5 0 0.9510 0.9039 0.8587 0.8154 0.7738 0.7339 0.6957 0.6591 0.640 0.5905 0.4437 0.377 0.373 0.1681 0.1160 0.0778 0.0503 0.0313 0 1 0.9990 0.996 0.9915 0.985 0.9774 0.9681 0.9575 0.9456 0.936 0.9185 0.835 0.7373 0.638 0.58 0.484 0.3370 0.56 0.1875 1 1.0000 0.9999 0.9997 0.9994 0.9988 0.9980 0.9969 0.9955 0.9937 0.9914 0.9734 0.941 0.8965 0.8369 0.7648 0.686 0.5931 0.5000 3 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9978 0.9933 0.9844 0.969 0.9460 0.9130 0.8688 0.815 3 4 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9990 0.9976 0.9947 0.9898 0.9815 0.9688 4 5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 = 6 0 0.9415 0.8858 0.8330 0.788 0.7351 0.6899 0.6470 0.6064 0.5679 0.5314 0.3771 0.61 0.1780 0.1176 0.0754 0.0467 0.077 0.0156 0 1 0.9985 0.9943 0.9875 0.9784 0.967 0.9541 0.939 0.97 0.9048 0.8857 0.7765 0.6554 0.5339 0.40 0.3191 0.333 0.1636 0.1094 1 1.0000 0.9998 0.9995 0.9988 0.9978 0.996 0.994 0.9915 0.988 0.984 0.957 0.9011 0.8306 0.7443 0.6471 0.5443 0.4415 0.3438 3 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.999 0.9987 0.9941 0.9830 0.964 0.995 0.886 0.808 0.7447 0.6563 3 4 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9984 0.9954 0.9891 0.9777 0.9590 0.9308 0.8906 4 5 1.0000 1.0000 0.9999 0.9998 0.9993 0.998 0.9959 0.9917 0.9844 5 6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 6 = 7 0 0.931 0.8681 0.8080 0.7514 0.6983 0.6485 0.6017 0.5578 0.5168 0.4783 0.306 0.097 0.1335 0.084 0.0490 0.080 0.015 0.0078 0 1 0.9980 0.991 0.989 0.9706 0.9556 0.938 0.9187 0.8974 0.8745 0.8503 0.7166 0.5767 0.4449 0.394 0.338 0.1586 0.104 0.065 1 1.0000 0.9997 0.9991 0.9980 0.996 0.9937 0.9903 0.9860 0.9807 0.9743 0.96 0.850 0.7564 0.6471 0.533 0.4199 0.3164 0.66 3 1.0000 1.0000 0.9999 0.9998 0.9996 0.9993 0.9988 0.998 0.9973 0.9879 0.9667 0.994 0.8740 0.800 0.710 0.6083 0.5000 3 4 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9988 0.9953 0.9871 0.971 0.9444 0.9037 0.8471 0.7734 4 5 1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.996 0.9910 0.981 0.9643 0.9375 5 6 1.0000 1.0000 0.9999 0.9998 0.9994 0.9984 0.9963 0.99 6 7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 7 = 8 0 0.97 0.8508 0.7837 0.714 0.6634 0.6096 0.5596 0.513 0.4703 0.4305 0.75 0.1678 0.1001 0.0576 0.0319 0.0168 0.0084 0.0039 0 1 0.9973 0.9897 0.9777 0.9619 0.948 0.908 0.8965 0.870 0.843 0.8131 0.657 0.5033 0.3671 0.553 0.1691 0.1064 0.063 0.035 1 0.9999 0.9996 0.9987 0.9969 0.994 0.9904 0.9853 0.9789 0.9711 0.9619 0.8948 0.7969 0.6785 0.5518 0.478 0.3154 0.01 0.1445 3 1.0000 1.0000 0.9999 0.9998 0.9996 0.9993 0.9987 0.9978 0.9966 0.9950 0.9786 0.9437 0.886 0.8059 0.7064 0.5941 0.4770 0.3633 3 4 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9996 0.9971 0.9896 0.977 0.940 0.8939 0.863 0.7396 0.6367 4 5 1.0000 1.0000 1.0000 1.0000 0.9998 0.9988 0.9958 0.9887 0.9747 0.950 0.9115 0.8555 5 6 1.0000 0.9999 0.9996 0.9987 0.9964 0.9915 0.9819 0.9648 6 7 1.0000 1.0000 0.9999 0.9998 0.9993 0.9983 0.9961 7 8 1.0000 1.0000 1.0000 1.0000 1.0000 8 8 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

p 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 0.50 p = 9 0 0.9135 0.8337 0.760 0.695 0.630 0.5730 0.504 0.47 0.479 0.3874 0.316 0.134 0.0751 0.0404 0.007 0.0101 0.0046 0.000 0 1 0.9966 0.9869 0.9718 0.95 0.988 0.90 0.879 0.8417 0.8088 0.7748 0.5995 0.436 0.3003 0.1960 0.111 0.0705 0.0385 0.0195 1 0.9999 0.9994 0.9980 0.9955 0.9916 0.986 0.9791 0.970 0.9595 0.9470 0.8591 0.738 0.6007 0.468 0.3373 0.318 0.1495 0.0898 3 1.0000 1.0000 0.9999 0.9997 0.9994 0.9987 0.9977 0.9963 0.9943 0.9917 0.9661 0.9144 0.8343 0.797 0.6089 0.486 0.3614 0.539 3 4 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9991 0.9944 0.9804 0.9511 0.901 0.883 0.7334 0.614 0.5000 4 5 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9969 0.9900 0.9747 0.9464 0.9006 0.834 0.7461 5 6 1.0000 1.0000 0.9997 0.9987 0.9957 0.9888 0.9750 0.950 0.910 6 7 1.0000 0.9999 0.9996 0.9986 0.996 0.9909 0.9805 7 8 1.0000 1.0000 0.9999 0.9997 0.999 0.9980 8 9 1.0000 1.0000 1.0000 1.0000 9 = 10 0 0.9044 0.8171 0.7374 0.6648 0.5987 0.5386 0.4840 0.4344 0.3894 0.3487 0.1969 0.1074 0.0563 0.08 0.0135 0.0060 0.005 0.0010 0 1 0.9957 0.9838 0.9655 0.9418 0.9139 0.884 0.8483 0.811 0.7746 0.7361 0.5443 0.3758 0.440 0.1493 0.0860 0.0464 0.033 0.0107 1 0.9999 0.9991 0.997 0.9938 0.9885 0.981 0.9717 0.9599 0.9460 0.998 0.80 0.6778 0.556 0.388 0.616 0.1673 0.0996 0.0547 3 1.0000 1.0000 0.9999 0.9996 0.9990 0.9980 0.9964 0.994 0.991 0.987 0.9500 0.8791 0.7759 0.6496 0.5138 0.383 0.660 0.1719 3 4 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9990 0.9984 0.9901 0.967 0.919 0.8497 0.7515 0.6331 0.5044 0.3770 4 5 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9986 0.9936 0.9803 0.957 0.9051 0.8338 0.7384 0.630 5 6 1.0000 1.0000 0.9999 0.9991 0.9965 0.9894 0.9740 0.945 0.8980 0.881 6 7 1.0000 0.9999 0.9996 0.9984 0.995 0.9877 0.976 0.9453 7 8 1.0000 1.0000 0.9999 0.9995 0.9983 0.9955 0.9893 8 9 1.0000 1.0000 0.9999 0.9997 0.9990 9 10 1.0000 1.0000 1.0000 10 = 11 0 0.8953 0.8007 0.7153 0.638 0.5688 0.5063 0.4501 0.3996 0.3544 0.3138 0.1673 0.0859 0.04 0.0198 0.0088 0.0036 0.0014 0.0005 0 1 0.9948 0.9805 0.9587 0.9308 0.8981 0.8618 0.88 0.7819 0.7399 0.6974 0.49 0.31 0.1971 0.1130 0.0606 0.030 0.0139 0.0059 1 0.9998 0.9988 0.9963 0.9917 0.9848 0.975 0.9630 0.9481 0.9305 0.9104 0.7788 0.6174 0.455 0.317 0.001 0.1189 0.065 0.037 3 1.0000 1.0000 0.9998 0.9993 0.9984 0.9970 0.9947 0.9915 0.9871 0.9815 0.9306 0.8389 0.7133 0.5696 0.456 0.963 0.1911 0.1133 3 4 1.0000 1.0000 0.9999 0.9997 0.9995 0.9990 0.9983 0.997 0.9841 0.9496 0.8854 0.7897 0.6683 0.538 0.3971 0.744 4 5 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9973 0.9883 0.9657 0.918 0.8513 0.7535 0.6331 0.5000 5 6 1.0000 1.0000 1.0000 0.9997 0.9980 0.994 0.9784 0.9499 0.9006 0.86 0.756 6 7 1.0000 0.9998 0.9988 0.9957 0.9878 0.9707 0.9390 0.8867 7 8 1.0000 0.9999 0.9994 0.9980 0.9941 0.985 0.9673 8 9 1.0000 1.0000 0.9998 0.9993 0.9978 0.9941 9 10 1.0000 1.0000 0.9998 0.9995 10 11 1.0000 11 = 1 0 0.8864 0.7847 0.6938 0.617 0.5404 0.4759 0.4186 0.3677 0.35 0.84 0.14 0.0687 0.0317 0.0138 0.0057 0.00 0.0008 0.000 0 1 0.9938 0.9769 0.9514 0.9191 0.8816 0.8405 0.7967 0.7513 0.705 0.6590 0.4435 0.749 0.1584 0.0850 0.044 0.0196 0.0083 0.003 1 0.9998 0.9985 0.995 0.9893 0.9804 0.9684 0.953 0.9348 0.9134 0.8891 0.7358 0.5583 0.3907 0.58 0.1513 0.0834 0.041 0.0193 3 1.0000 0.9999 0.9997 0.9990 0.9978 0.9957 0.995 0.9880 0.980 0.9744 0.9078 0.7946 0.6488 0.495 0.3467 0.53 0.1345 0.0730 3 4 1.0000 1.0000 0.9999 0.9998 0.9996 0.9991 0.9984 0.9973 0.9957 0.9761 0.974 0.844 0.737 0.5833 0.438 0.3044 0.1938 4 5 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9954 0.9806 0.9456 0.88 0.7873 0.665 0.569 0.387 5 6 1.0000 1.0000 1.0000 0.9999 0.9993 0.9961 0.9857 0.9614 0.9154 0.8418 0.7393 0.618 6 7 1.0000 0.9999 0.9994 0.997 0.9905 0.9745 0.947 0.8883 0.806 7 8 1.0000 0.9999 0.9996 0.9983 0.9944 0.9847 0.9644 0.970 8 9 1.0000 1.0000 0.9998 0.999 0.997 0.991 0.9807 9 10 1.0000 0.9999 0.9997 0.9989 0.9968 10 11 1.0000 1.0000 0.9999 0.9998 11 1 1.0000 1.0000 1 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 9

p 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 0.50 p = 13 0 0.8775 0.7690 0.6730 0.588 0.5133 0.4474 0.3893 0.3383 0.935 0.54 0.109 0.0550 0.038 0.0097 0.0037 0.0013 0.0004 0.0001 0 1 0.998 0.9730 0.9436 0.9068 0.8646 0.8186 0.770 0.706 0.6707 0.613 0.3983 0.336 0.167 0.0637 0.096 0.016 0.0049 0.0017 1 0.9997 0.9980 0.9938 0.9865 0.9755 0.9608 0.94 0.901 0.8946 0.8661 0.690 0.5017 0.336 0.05 0.113 0.0579 0.069 0.011 3 1.0000 0.9999 0.9995 0.9986 0.9969 0.9940 0.9897 0.9837 0.9758 0.9658 0.880 0.7473 0.5843 0.406 0.783 0.1686 0.099 0.0461 3 4 1.0000 1.0000 0.9999 0.9997 0.9993 0.9987 0.9976 0.9959 0.9935 0.9658 0.9009 0.7940 0.6543 0.5005 0.3530 0.79 0.1334 4 5 1.0000 1.0000 0.9999 0.9999 0.9997 0.9995 0.9991 0.995 0.9700 0.9198 0.8346 0.7159 0.5744 0.468 0.905 5 6 1.0000 1.0000 1.0000 0.9999 0.9999 0.9987 0.9930 0.9757 0.9376 0.8705 0.771 0.6437 0.5000 6 7 1.0000 1.0000 0.9998 0.9988 0.9944 0.9818 0.9538 0.903 0.81 0.7095 7 8 1.0000 0.9998 0.9990 0.9960 0.9874 0.9679 0.930 0.8666 8 9 1.0000 0.9999 0.9993 0.9975 0.99 0.9797 0.9539 9 10 1.0000 0.9999 0.9997 0.9987 0.9959 0.9888 10 11 1.0000 1.0000 0.9999 0.9995 0.9983 11 1 1.0000 1.0000 0.9999 1 13 1.0000 13 = 14 0 0.8687 0.7536 0.658 0.5647 0.4877 0.405 0.360 0.311 0.670 0.88 0.108 0.0440 0.0178 0.0068 0.004 0.0008 0.000 0.0001 0 1 0.9916 0.9690 0.9355 0.8941 0.8470 0.7963 0.7436 0.6900 0.6368 0.5846 0.3567 0.1979 0.1010 0.0475 0.005 0.0081 0.009 0.0009 1 0.9997 0.9975 0.993 0.9833 0.9699 0.95 0.930 0.904 0.8745 0.8416 0.6479 0.4481 0.811 0.1608 0.0839 0.0398 0.0170 0.0065 3 1.0000 0.9999 0.9994 0.9981 0.9958 0.990 0.9864 0.9786 0.9685 0.9559 0.8535 0.698 0.513 0.355 0.05 0.143 0.063 0.087 3 4 1.0000 1.0000 0.9998 0.9996 0.9990 0.9980 0.9965 0.9941 0.9908 0.9533 0.870 0.7415 0.584 0.47 0.793 0.167 0.0898 4 5 1.0000 1.0000 0.9999 0.9998 0.9996 0.999 0.9985 0.9885 0.9561 0.8883 0.7805 0.6405 0.4859 0.3373 0.10 5 6 1.0000 1.0000 1.0000 0.9999 0.9998 0.9978 0.9884 0.9617 0.9067 0.8164 0.695 0.5461 0.3953 6 7 1.0000 1.0000 0.9997 0.9976 0.9897 0.9685 0.947 0.8499 0.7414 0.6047 7 8 1.0000 0.9996 0.9978 0.9917 0.9757 0.9417 0.8811 0.7880 8 9 1.0000 0.9997 0.9983 0.9940 0.985 0.9574 0.910 9 10 1.0000 0.9998 0.9989 0.9961 0.9886 0.9713 10 11 1.0000 0.9999 0.9994 0.9978 0.9935 11 1 1.0000 0.9999 0.9997 0.9991 1 13 1.0000 1.0000 0.9999 13 14 1.0000 14 = 15 0 0.8601 0.7386 0.6333 0.541 0.4633 0.3953 0.3367 0.863 0.430 0.059 0.0874 0.035 0.0134 0.0047 0.0016 0.0005 0.0001 0.0000 0 1 0.9904 0.9647 0.970 0.8809 0.890 0.7738 0.7168 0.6597 0.6035 0.5490 0.3186 0.1671 0.080 0.0353 0.014 0.005 0.0017 0.0005 1 0.9996 0.9970 0.9906 0.9797 0.9638 0.949 0.9171 0.8870 0.8531 0.8159 0.604 0.3980 0.361 0.168 0.0617 0.071 0.0107 0.0037 3 1.0000 0.9998 0.999 0.9976 0.9945 0.9896 0.985 0.977 0.9601 0.9444 0.87 0.648 0.4613 0.969 0.177 0.0905 0.044 0.0176 3 4 1.0000 0.9999 0.9998 0.9994 0.9986 0.997 0.9950 0.9918 0.9873 0.9383 0.8358 0.6865 0.5155 0.3519 0.173 0.104 0.059 4 5 1.0000 1.0000 0.9999 0.9999 0.9997 0.9993 0.9987 0.9978 0.983 0.9389 0.8516 0.716 0.5643 0.403 0.608 0.1509 5 6 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9964 0.9819 0.9434 0.8689 0.7548 0.6098 0.45 0.3036 6 7 1.0000 1.0000 1.0000 0.9994 0.9958 0.987 0.9500 0.8868 0.7869 0.6535 0.5000 7 8 0.9999 0.999 0.9958 0.9848 0.9578 0.9050 0.818 0.6964 8 9 1.0000 0.9999 0.999 0.9963 0.9876 0.966 0.931 0.8491 9 10 1.0000 0.9999 0.9993 0.997 0.9907 0.9745 0.9408 10 11 1.0000 0.9999 0.9995 0.9981 0.9937 0.984 11 1 1.0000 0.9999 0.9997 0.9989 0.9963 1 13 1.0000 1.0000 0.9999 0.9995 13 14 1.0000 1.0000 14 10 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

p 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 0.50 p = 0 0 0.8179 0.6676 0.5438 0.440 0.3585 0.901 0.34 0.1887 0.1516 0.116 0.0388 0.0115 0.003 0.0008 0.000 0.0000 0.0000 0.0000 0 1 0.9831 0.9401 0.880 0.8103 0.7358 0.6605 0.5869 0.5169 0.4516 0.3917 0.1756 0.069 0.043 0.0076 0.001 0.0005 0.0001 0.0000 1 0.9990 0.999 0.9790 0.9561 0.945 0.8850 0.8390 0.7879 0.7334 0.6769 0.4049 0.061 0.0913 0.0355 0.011 0.0036 0.0009 0.000 3 1.0000 0.9994 0.9973 0.996 0.9841 0.9710 0.959 0.994 0.9007 0.8670 0.6477 0.4114 0.5 0.1071 0.0444 0.0160 0.0049 0.0013 3 4 1.0000 0.9997 0.9990 0.9974 0.9944 0.9893 0.9817 0.9710 0.9568 0.898 0.696 0.4148 0.375 0.118 0.0510 0.0189 0.0059 4 5 1.0000 0.9999 0.9997 0.9991 0.9981 0.996 0.993 0.9887 0.937 0.804 0.617 0.4164 0.454 0.156 0.0553 0.007 5 6 1.0000 1.0000 0.9999 0.9997 0.9994 0.9987 0.9976 0.9781 0.9133 0.7858 0.6080 0.4166 0.500 0.199 0.0577 6 7 1.0000 1.0000 0.9999 0.9998 0.9996 0.9941 0.9679 0.898 0.773 0.6010 0.4159 0.50 0.1316 7 8 1.0000 1.0000 0.9999 0.9987 0.9900 0.9591 0.8867 0.764 0.5956 0.4143 0.517 8 9 1.0000 0.9998 0.9974 0.9861 0.950 0.878 0.7553 0.5914 0.4119 9 10 1.0000 0.9994 0.9961 0.989 0.9468 0.875 0.7507 0.5881 10 11 0.9999 0.9991 0.9949 0.9804 0.9435 0.869 0.7483 11 1 1.0000 0.9998 0.9987 0.9940 0.9790 0.940 0.8684 1 13 1.0000 0.9997 0.9985 0.9935 0.9786 0.943 13 14 1.0000 0.9997 0.9984 0.9936 0.9793 14 15 1.0000 0.9997 0.9985 0.9941 15 16 1.0000 0.9997 0.9987 16 17 1.0000 0.9998 17 18 1.0000 18 = 5 0 0.7778 0.6035 0.4670 0.3604 0.774 0.19 0.1630 0.144 0.0946 0.0718 0.017 0.0038 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0 1 0.974 0.9114 0.880 0.7358 0.644 0.557 0.4696 0.3947 0.386 0.71 0.0931 0.074 0.0070 0.0016 0.0003 0.0001 0.0000 0.0000 1 0.9980 0.9868 0.960 0.935 0.879 0.819 0.7466 0.6768 0.6063 0.5371 0.537 0.098 0.031 0.0090 0.001 0.0004 0.0001 0.0000 3 0.9999 0.9986 0.9938 0.9835 0.9659 0.940 0.9064 0.8649 0.8169 0.7636 0.4711 0.340 0.096 0.033 0.0097 0.004 0.0005 0.0001 3 4 1.0000 0.9999 0.999 0.997 0.998 0.9850 0.976 0.9549 0.9314 0.900 0.681 0.407 0.137 0.0905 0.030 0.0095 0.003 0.0005 4 5 1.0000 0.9999 0.9996 0.9988 0.9969 0.9935 0.9877 0.9790 0.9666 0.8385 0.6167 0.3783 0.1935 0.086 0.094 0.0086 0.000 5 6 1.0000 1.0000 0.9998 0.9995 0.9987 0.997 0.9946 0.9905 0.9305 0.7800 0.5611 0.3407 0.1734 0.0736 0.058 0.0073 6 7 1.0000 0.9999 0.9998 0.9995 0.9989 0.9977 0.9745 0.8909 0.765 0.5118 0.3061 0.1536 0.0639 0.016 7 8 1.0000 1.0000 0.9999 0.9998 0.9995 0.990 0.953 0.8506 0.6769 0.4668 0.735 0.1340 0.0539 8 9 1.0000 1.0000 0.9999 0.9979 0.987 0.987 0.8106 0.6303 0.446 0.44 0.1148 9 10 1.0000 0.9995 0.9944 0.9703 0.90 0.771 0.5858 0.3843 0.1 10 11 0.9999 0.9985 0.9893 0.9558 0.8746 0.733 0.546 0.3450 11 1 1.0000 0.9996 0.9966 0.985 0.9396 0.846 0.6937 0.5000 1 13 0.9999 0.9991 0.9940 0.9745 0.9 0.8173 0.6550 13 14 1.0000 0.9998 0.998 0.9907 0.9656 0.9040 0.7878 14 15 1.0000 0.9995 0.9971 0.9868 0.9560 0.885 15 16 0.9999 0.999 0.9957 0.986 0.9461 16 17 1.0000 0.9998 0.9988 0.994 0.9784 17 18 1.0000 0.9997 0.9984 0.997 18 19 0.9999 0.9996 0.9980 19 0 1.0000 0.9999 0.9995 0 1 1.0000 0.9999 1 1.0000 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 11

p 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 0.50 p = 30 0 0.7397 0.5455 0.4010 0.939 0.146 0.1563 0.1134 0.080 0.0591 0.044 0.0076 0.001 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0 1 0.9639 0.8795 0.7731 0.661 0.5535 0.4555 0.3694 0.958 0.343 0.1837 0.0480 0.0105 0.000 0.0003 0.0000 0.0000 0.0000 0.0000 1 0.9967 0.9783 0.9399 0.8831 0.81 0.734 0.6487 0.5654 0.4855 0.4114 0.1514 0.044 0.0106 0.001 0.0003 0.0000 0.0000 0.0000 3 0.9998 0.9971 0.9881 0.9694 0.939 0.8974 0.8450 0.784 0.7175 0.6474 0.317 0.17 0.0374 0.0093 0.0019 0.0003 0.0000 0.0000 3 4 1.0000 0.9997 0.998 0.9937 0.9844 0.9685 0.9447 0.916 0.873 0.845 0.545 0.55 0.0979 0.030 0.0075 0.0015 0.000 0.0000 4 5 1.0000 0.9998 0.9989 0.9967 0.991 0.9838 0.9707 0.9519 0.968 0.7106 0.475 0.06 0.0766 0.033 0.0057 0.0011 0.000 5 6 1.0000 0.9999 0.9994 0.9983 0.9960 0.9918 0.9848 0.974 0.8474 0.6070 0.3481 0.1595 0.0586 0.017 0.0040 0.0007 6 7 1.0000 0.9999 0.9997 0.999 0.9980 0.9959 0.99 0.930 0.7608 0.5143 0.814 0.138 0.0435 0.011 0.006 7 8 1.0000 1.0000 0.9999 0.9996 0.9990 0.9980 0.97 0.8713 0.6736 0.4315 0.47 0.0940 0.031 0.0081 8 9 1.0000 0.9999 0.9998 0.9995 0.9903 0.9389 0.8034 0.5888 0.3575 0.1763 0.0694 0.014 9 10 1.0000 1.0000 0.9999 0.9971 0.9744 0.8943 0.7304 0.5078 0.915 0.1350 0.0494 10 11 1.0000 0.999 0.9905 0.9493 0.8407 0.6548 0.4311 0.37 0.100 11 1 0.9998 0.9969 0.9784 0.9155 0.780 0.5785 0.359 0.1808 1 13 1.0000 0.9991 0.9918 0.9599 0.8737 0.7145 0.505 0.93 13 14 0.9998 0.9973 0.9831 0.9348 0.846 0.6448 0.478 14 15 0.9999 0.999 0.9936 0.9699 0.909 0.7691 0.57 15 16 1.0000 0.9998 0.9979 0.9876 0.9519 0.8644 0.7077 16 17 0.9999 0.9994 0.9955 0.9788 0.986 0.819 17 18 1.0000 0.9998 0.9986 0.9917 0.9666 0.8998 18 19 1.0000 0.9996 0.9971 0.986 0.9506 19 0 0.9999 0.9991 0.9950 0.9786 0 1 1.0000 0.9998 0.9984 0.9919 1 1.0000 0.9996 0.9974 3 0.9999 0.9993 3 4 1.0000 0.9998 4 5 1.0000 5 1 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

p 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 0.50 p = 40 0 0.6690 0.4457 0.957 0.1954 0.185 0.084 0.0549 0.0356 0.030 0.0148 0.0015 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 1 0.9393 0.8095 0.6615 0.510 0.3991 0.990 0.01 0.1594 0.1140 0.0805 0.011 0.0015 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.995 0.9543 0.88 0.7855 0.6767 0.5665 0.465 0.3694 0.894 0.8 0.0486 0.0079 0.0010 0.0001 0.0000 0.0000 0.0000 0.0000 3 0.9993 0.9918 0.9686 0.95 0.8619 0.787 0.6937 0.6007 0.509 0.431 0.130 0.085 0.0047 0.0006 0.0001 0.0000 0.0000 0.0000 3 4 1.0000 0.9988 0.9933 0.9790 0.950 0.9104 0.8546 0.7868 0.7103 0.690 0.633 0.0759 0.0160 0.006 0.0003 0.0000 0.0000 0.0000 4 5 0.9999 0.9988 0.9951 0.9861 0.9691 0.9419 0.9033 0.8535 0.7937 0.435 0.1613 0.0433 0.0086 0.0013 0.0001 0.0000 0.0000 5 6 1.0000 0.9998 0.9990 0.9966 0.9909 0.9801 0.964 0.9361 0.9005 0.6067 0.859 0.096 0.038 0.0044 0.0006 0.0001 0.0000 6 7 1.0000 0.9998 0.9993 0.9977 0.994 0.9873 0.9758 0.9581 0.7559 0.4371 0.180 0.0553 0.014 0.001 0.000 0.0000 7 8 1.0000 0.9999 0.9995 0.9985 0.9963 0.9919 0.9845 0.8646 0.5931 0.998 0.1110 0.0303 0.0061 0.0009 0.0001 8 9 1.0000 0.9999 0.9997 0.9990 0.9976 0.9949 0.938 0.7318 0.4395 0.1959 0.0644 0.0156 0.007 0.0003 9 10 1.0000 0.9999 0.9998 0.9994 0.9985 0.9701 0.839 0.5839 0.3087 0.115 0.035 0.0074 0.0011 10 11 1.0000 1.0000 0.9999 0.9996 0.9880 0.915 0.7151 0.4406 0.053 0.0709 0.0179 0.003 11 1 1.0000 0.9999 0.9957 0.9568 0.809 0.577 0.3143 0.185 0.0386 0.0083 1 13 1.0000 0.9986 0.9806 0.8968 0.703 0.4408 0.11 0.0751 0.019 13 14 0.9996 0.991 0.9456 0.8074 0.571 0.3174 0.136 0.0403 14 15 0.9999 0.9971 0.9738 0.8849 0.6946 0.440 0.14 0.0769 15 16 1.0000 0.9990 0.9884 0.9367 0.7978 0.5681 0.3185 0.1341 16 17 0.9997 0.9953 0.9680 0.8761 0.6885 0.4391 0.148 17 18 0.9999 0.9983 0.985 0.9301 0.7911 0.5651 0.3179 18 19 1.0000 0.9994 0.9937 0.9637 0.870 0.6844 0.4373 19 0 0.9998 0.9976 0.987 0.956 0.7870 0.567 0 1 1.0000 0.9991 0.995 0.9608 0.8669 0.681 1 0.9997 0.9970 0.9811 0.933 0.785 3 0.9999 0.9989 0.9917 0.9595 0.8659 3 4 1.0000 0.9996 0.9966 0.9804 0.931 4 5 0.9999 0.9988 0.9914 0.9597 5 6 1.0000 0.9996 0.9966 0.9808 6 7 0.9999 0.9988 0.9917 7 8 1.0000 0.9996 0.9968 8 9 0.9999 0.9989 9 30 1.0000 0.9997 30 31 0.9999 31 3 1.0000 3 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 13

p 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 0.50 p = 50 0 0.6050 0.364 0.181 0.199 0.0769 0.0453 0.066 0.0155 0.0090 0.005 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 1 0.9106 0.7358 0.5553 0.4005 0.794 0.1900 0.165 0.087 0.053 0.0338 0.009 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.986 0.916 0.8108 0.6767 0.5405 0.416 0.3108 0.60 0.1605 0.1117 0.014 0.0013 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 3 0.9984 0.98 0.937 0.8609 0.7604 0.6473 0.537 0.453 0.3303 0.503 0.0460 0.0057 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 3 4 0.9999 0.9968 0.983 0.9510 0.8964 0.806 0.790 0.690 0.577 0.431 0.111 0.0185 0.001 0.000 0.0000 0.0000 0.0000 0.0000 4 5 1.0000 0.9995 0.9963 0.9856 0.96 0.94 0.8650 0.7919 0.707 0.6161 0.194 0.0480 0.0070 0.0007 0.0001 0.0000 0.0000 0.0000 5 6 0.9999 0.9993 0.9964 0.988 0.9711 0.9417 0.8981 0.8404 0.770 0.3613 0.1034 0.0194 0.005 0.000 0.0000 0.0000 0.0000 6 7 1.0000 0.9999 0.999 0.9968 0.9906 0.9780 0.956 0.93 0.8779 0.5188 0.1904 0.0453 0.0073 0.0008 0.0001 0.0000 0.0000 7 8 1.0000 0.9999 0.999 0.9973 0.997 0.9833 0.967 0.941 0.6681 0.3073 0.0916 0.0183 0.005 0.000 0.0000 0.0000 8 9 1.0000 0.9998 0.9993 0.9978 0.9944 0.9875 0.9755 0.7911 0.4437 0.1637 0.040 0.0067 0.0008 0.0001 0.0000 9 10 1.0000 0.9998 0.9994 0.9983 0.9957 0.9906 0.8801 0.5836 0.6 0.0789 0.0160 0.00 0.000 0.0000 10 11 1.0000 0.9999 0.9995 0.9987 0.9968 0.937 0.7107 0.3816 0.1390 0.034 0.0057 0.0006 0.0000 11 1 1.0000 0.9999 0.9996 0.9990 0.9699 0.8139 0.5110 0.9 0.0661 0.0133 0.0018 0.000 1 13 1.0000 0.9999 0.9997 0.9868 0.8894 0.6370 0.379 0.1163 0.080 0.0045 0.0005 13 14 1.0000 0.9999 0.9947 0.9393 0.7481 0.4468 0.1878 0.0540 0.0104 0.0013 14 15 1.0000 0.9981 0.969 0.8369 0.569 0.801 0.0955 0.00 0.0033 15 16 0.9993 0.9856 0.9017 0.6839 0.3889 0.1561 0.047 0.0077 16 17 0.9998 0.9937 0.9449 0.78 0.5060 0.369 0.0765 0.0164 17 18 0.9999 0.9975 0.9713 0.8594 0.616 0.3356 0.173 0.035 18 19 1.0000 0.9991 0.9861 0.915 0.764 0.4465 0.1974 0.0595 19 0 0.9997 0.9937 0.95 0.8139 0.5610 0.86 0.1013 0 1 0.9999 0.9974 0.9749 0.8813 0.6701 0.3900 0.1611 1 1.0000 0.9990 0.9877 0.990 0.7660 0.5019 0.399 3 0.9996 0.9944 0.9604 0.8438 0.6134 0.3359 3 4 0.9999 0.9976 0.9793 0.90 0.7160 0.4439 4 5 1.0000 0.9991 0.9900 0.947 0.8034 0.5561 5 6 0.9997 0.9955 0.9686 0.871 0.6641 6 7 0.9999 0.9981 0.9840 0.90 0.7601 7 8 1.0000 0.9993 0.994 0.9556 0.8389 8 9 0.9997 0.9966 0.9765 0.8987 9 30 0.9999 0.9986 0.9884 0.9405 30 31 1.0000 0.9995 0.9947 0.9675 31 3 0.9998 0.9978 0.9836 3 33 0.9999 0.9991 0.993 33 34 1.0000 0.9997 0.9967 34 35 0.9999 0.9987 35 36 1.0000 0.9995 36 37 0.9998 37 38 1.0000 38 14 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

Table : Cumulative Poisso Distributio Fuctio The tabulated value is P(X ), where X has a Poisso distributio with mea λ. λ 0.10 0.0 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0 1. 1.4 1.6 1.8 λ 0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066 0.3679 0.301 0.466 0.019 0.1653 0 1 0.9953 0.985 0.9631 0.9384 0.9098 0.8781 0.844 0.8088 0.775 0.7358 0.666 0.5918 0.549 0.468 1 0.9998 0.9989 0.9964 0.991 0.9856 0.9769 0.9659 0.956 0.9371 0.9197 0.8795 0.8335 0.7834 0.7306 3 1.0000 0.9999 0.9997 0.999 0.998 0.9966 0.994 0.9909 0.9865 0.9810 0.966 0.9463 0.91 0.8913 3 4 1.0000 1.0000 0.9999 0.9998 0.9996 0.999 0.9986 0.9977 0.9963 0.993 0.9857 0.9763 0.9636 4 5 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9985 0.9968 0.9940 0.9896 5 6 1.0000 1.0000 1.0000 0.9999 0.9997 0.9994 0.9987 0.9974 6 7 1.0000 1.0000 0.9999 0.9997 0.9994 7 8 1.0000 1.0000 0.9999 8 9 1.0000 9 λ.0..4.6.8 3.0 3. 3.4 3.6 3.8 4.0 4.5 5.0 5.5 λ 0 0.1353 0.1108 0.0907 0.0743 0.0608 0.0498 0.0408 0.0334 0.073 0.04 0.0183 0.0111 0.0067 0.0041 0 1 0.4060 0.3546 0.3084 0.674 0.311 0.1991 0.171 0.1468 0.157 0.1074 0.0916 0.0611 0.0404 0.066 1 0.6767 0.67 0.5697 0.5184 0.4695 0.43 0.3799 0.3397 0.307 0.689 0.381 0.1736 0.147 0.0884 3 0.8571 0.8194 0.7787 0.7360 0.6919 0.647 0.605 0.5584 0.515 0.4735 0.4335 0.343 0.650 0.017 3 4 0.9473 0.975 0.9041 0.8774 0.8477 0.8153 0.7806 0.744 0.7064 0.6678 0.688 0.531 0.4405 0.3575 4 5 0.9834 0.9751 0.9643 0.9510 0.9349 0.9161 0.8946 0.8705 0.8441 0.8156 0.7851 0.709 0.6160 0.589 5 6 0.9955 0.995 0.9884 0.988 0.9756 0.9665 0.9554 0.941 0.967 0.9091 0.8893 0.8311 0.76 0.6860 6 7 0.9989 0.9980 0.9967 0.9947 0.9919 0.9881 0.983 0.9769 0.969 0.9599 0.9489 0.9134 0.8666 0.8095 7 λ.0..4.6.8 3.0 3. 3.4 3.6 3.8 4.0 4.5 5.0 5.5 λ 8 0.9998 0.9995 0.9991 0.9985 0.9976 0.996 0.9943 0.9917 0.9883 0.9840 0.9786 0.9597 0.9319 0.8944 8 9 1.0000 0.9999 0.9998 0.9996 0.9993 0.9989 0.998 0.9973 0.9960 0.994 0.9919 0.989 0.968 0.946 9 10 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.999 0.9987 0.9981 0.997 0.9933 0.9863 0.9747 10 11 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9994 0.9991 0.9976 0.9945 0.9890 11 1 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.999 0.9980 0.9955 1 13 1.0000 1.0000 1.0000 0.9999 0.9997 0.9993 0.9983 13 14 1.0000 0.9999 0.9998 0.9994 14 15 1.0000 0.9999 0.9998 15 16 1.0000 0.9999 16 17 1.0000 17 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 15

λ 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 11.0 1.0 13.0 14.0 15.0 λ 0 0.005 0.0015 0.0009 0.0006 0.0003 0.000 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 1 0.0174 0.0113 0.0073 0.0047 0.0030 0.0019 0.001 0.0008 0.0005 0.000 0.0001 0.0000 0.0000 0.0000 1 0.060 0.0430 0.096 0.003 0.0138 0.0093 0.006 0.004 0.008 0.001 0.0005 0.000 0.0001 0.0000 3 0.151 0.1118 0.0818 0.0591 0.044 0.0301 0.01 0.0149 0.0103 0.0049 0.003 0.0011 0.0005 0.000 3 4 0.851 0.37 0.1730 0.131 0.0996 0.0744 0.0550 0.0403 0.093 0.0151 0.0076 0.0037 0.0018 0.0009 4 5 0.4457 0.3690 0.3007 0.414 0.191 0.1496 0.1157 0.0885 0.0671 0.0375 0.003 0.0107 0.0055 0.008 5 6 0.6063 0.565 0.4497 0.378 0.3134 0.56 0.068 0.1649 0.1301 0.0786 0.0458 0.059 0.014 0.0076 6 7 0.7440 0.678 0.5987 0.546 0.4530 0.3856 0.339 0.687 0.0 0.143 0.0895 0.0540 0.0316 0.0180 7 8 0.847 0.7916 0.791 0.660 0.595 0.531 0.4557 0.3918 0.338 0.30 0.1550 0.0998 0.061 0.0374 8 9 0.9161 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.518 0.4579 0.3405 0.44 0.1658 0.1094 0.0699 9 10 0.9574 0.933 0.9015 0.86 0.8159 0.7634 0.7060 0.6453 0.5830 0.4599 0.347 0.517 0.1757 0.1185 10 11 0.9799 0.9661 0.9467 0.908 0.8881 0.8487 0.8030 0.750 0.6968 0.5793 0.4616 0.353 0.600 0.1848 11 1 0.991 0.9840 0.9730 0.9573 0.936 0.9091 0.8758 0.8364 0.7916 0.6887 0.5760 0.4631 0.3585 0.676 1 13 0.9964 0.999 0.987 0.9784 0.9658 0.9486 0.961 0.8981 0.8645 0.7813 0.6815 0.5730 0.4644 0.363 13 14 0.9986 0.9970 0.9943 0.9897 0.987 0.976 0.9585 0.9400 0.9165 0.8540 0.770 0.6751 0.5704 0.4657 14 15 0.9995 0.9988 0.9976 0.9954 0.9918 0.986 0.9780 0.9665 0.9513 0.9074 0.8444 0.7636 0.6694 0.5681 15 16 0.9998 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.983 0.9730 0.9441 0.8987 0.8355 0.7559 0.6641 16 17 0.9999 0.9998 0.9996 0.999 0.9984 0.9970 0.9947 0.9911 0.9857 0.9678 0.9370 0.8905 0.87 0.7489 17 18 1.0000 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.9957 0.998 0.983 0.966 0.930 0.886 0.8195 18 19 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.9980 0.9965 0.9907 0.9787 0.9573 0.935 0.875 19 0 1.0000 0.9999 0.9998 0.9996 0.9991 0.9984 0.9953 0.9884 0.9750 0.951 0.9170 0 1 1.0000 0.9999 0.9998 0.9996 0.9993 0.9977 0.9939 0.9859 0.971 0.9469 1 1.0000 0.9999 0.9999 0.9997 0.9990 0.9970 0.994 0.9833 0.9673 3 1.0000 0.9999 0.9999 0.9995 0.9985 0.9960 0.9907 0.9805 3 4 1.0000 1.0000 0.9998 0.9993 0.9980 0.9950 0.9888 4 5 0.9999 0.9997 0.9990 0.9974 0.9938 5 6 1.0000 0.9999 0.9995 0.9987 0.9967 6 7 0.9999 0.9998 0.9994 0.9983 7 8 1.0000 0.9999 0.9997 0.9991 8 9 1.0000 0.9999 0.9996 9 30 0.9999 0.9998 30 31 1.0000 0.9999 31 3 1.0000 3 16 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

Table 3: Normal Distributio Fuctio The table gives the probability, p, that a ormally distributed radom variable Z, with mea = 0 ad variace = 1, is less tha or equal to z. z 0.00 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 z 0.0 0.50000 0.50399 0.50798 0.51197 0.51595 0.51994 0.539 0.5790 0.53188 0.53586 0.0 0.1 0.53983 0.54380 0.54776 0.5517 0.55567 0.5596 0.56356 0.56749 0.5714 0.57535 0.1 0. 0.5796 0.58317 0.58706 0.59095 0.59483 0.59871 0.6057 0.6064 0.6106 0.61409 0. 0.3 0.61791 0.617 0.655 0.6930 0.63307 0.63683 0.64058 0.64431 0.64803 0.65173 0.3 0.4 0.6554 0.65910 0.6676 0.66640 0.67003 0.67364 0.6774 0.6808 0.68439 0.68793 0.4 0.5 0.69146 0.69497 0.69847 0.70194 0.70540 0.70884 0.716 0.71566 0.71904 0.740 0.5 0.6 0.7575 0.7907 0.7337 0.73565 0.73891 0.7415 0.74537 0.74857 0.75175 0.75490 0.6 0.7 0.75804 0.76115 0.7644 0.76730 0.77035 0.77337 0.77637 0.77935 0.7830 0.7854 0.7 0.8 0.78814 0.79103 0.79389 0.79673 0.79955 0.8034 0.80511 0.80785 0.81057 0.8137 0.8 0.9 0.81594 0.81859 0.811 0.8381 0.8639 0.8894 0.83147 0.83398 0.83646 0.83891 0.9 1.0 0.84134 0.84375 0.84614 0.84849 0.85083 0.85314 0.85543 0.85769 0.85993 0.8614 1.0 1.1 0.86433 0.86650 0.86864 0.87076 0.8786 0.87493 0.87698 0.87900 0.88100 0.8898 1.1 1. 0.88493 0.88686 0.88877 0.89065 0.8951 0.89435 0.89617 0.89796 0.89973 0.90147 1. 1.3 0.9030 0.90490 0.90658 0.9084 0.90988 0.91149 0.91309 0.91466 0.9161 0.91774 1.3 1.4 0.9194 0.9073 0.90 0.9364 0.9507 0.9647 0.9785 0.99 0.93056 0.93189 1.4 1.5 0.93319 0.93448 0.93574 0.93699 0.938 0.93943 0.9406 0.94179 0.9495 0.94408 1.5 1.6 0.9450 0.94630 0.94738 0.94845 0.94950 0.95053 0.95154 0.9554 0.9535 0.95449 1.6 1.7 0.95543 0.95637 0.9578 0.95818 0.95907 0.95994 0.96080 0.96164 0.9646 0.9637 1.7 1.8 0.96407 0.96485 0.9656 0.96638 0.9671 0.96784 0.96856 0.9696 0.96995 0.9706 1.8 1.9 0.9718 0.97193 0.9757 0.9730 0.97381 0.97441 0.97500 0.97558 0.97615 0.97670 1.9.0 0.9775 0.97778 0.97831 0.9788 0.9793 0.9798 0.98030 0.98077 0.9814 0.98169.0.1 0.9814 0.9857 0.98300 0.98341 0.9838 0.984 0.98461 0.98500 0.98537 0.98574.1. 0.98610 0.98645 0.98679 0.98713 0.98745 0.98778 0.98809 0.98840 0.98870 0.98899..3 0.9898 0.98956 0.98983 0.99010 0.99036 0.99061 0.99086 0.99111 0.99134 0.99158.3.4 0.99180 0.990 0.994 0.9945 0.9966 0.9986 0.99305 0.9934 0.99343 0.99361.4.5 0.99379 0.99396 0.99413 0.99430 0.99446 0.99461 0.99477 0.9949 0.99506 0.9950.5.6 0.99534 0.99547 0.99560 0.99573 0.99585 0.99598 0.99609 0.9961 0.9963 0.99643.6.7 0.99653 0.99664 0.99674 0.99683 0.99693 0.9970 0.99711 0.9970 0.9978 0.99736.7.8 0.99744 0.9975 0.99760 0.99767 0.99774 0.99781 0.99788 0.99795 0.99801 0.99807.8.9 0.99813 0.99819 0.9985 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861.9 3.0 0.99865 0.99869 0.99874 0.99878 0.9988 0.99886 0.99889 0.99893 0.99896 0.99900 3.0 3.1 0.99903 0.99906 0.99910 0.99913 0.99916 0.99918 0.9991 0.9994 0.9996 0.9999 3.1 3. 0.99931 0.99934 0.99936 0.99938 0.99940 0.9994 0.99944 0.99946 0.99948 0.99950 3. 3.3 0.9995 0.99953 0.99955 0.99957 0.99958 0.99960 0.99961 0.9996 0.99964 0.99965 3.3 3.4 0.99966 0.99968 0.99969 0.99970 0.99971 0.9997 0.99973 0.99974 0.99975 0.99976 3.4 3.5 0.99977 0.99978 0.99978 0.99979 0.99980 0.99981 0.99981 0.9998 0.99983 0.99983 3.5 3.6 0.99984 0.99985 0.99985 0.99986 0.99986 0.99987 0.99987 0.99988 0.99988 0.99989 3.6 3.7 0.99989 0.99990 0.99990 0.99990 0.99991 0.99991 0.9999 0.9999 0.9999 0.9999 3.7 3.8 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.99995 3.8 3.9 0.99995 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997 3.9 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 17

Table 4: Percetage Poits of the Normal Distributio The table gives the values of z satisfyig P(Z z) = p, where Z is the ormally distributed radom variable with mea = 0 ad variace = 1. p 0.00 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 p 0.5 0.0000 0.051 0.050 0.0753 0.1004 0.157 0.1510 0.1764 0.019 0.75 0.5 0.6 0.533 0.793 0.3055 0.3319 0.3585 0.3853 0.415 0.4399 0.4677 0.4958 0.6 0.7 0.544 0.5534 0.588 0.618 0.6433 0.6745 0.7063 0.7388 0.77 0.8064 0.7 0.8 0.8416 0.8779 0.9154 0.954 0.9945 1.0364 1.0803 1.164 1.1750 1.65 0.8 0.9 1.816 1.3408 1.4051 1.4758 1.5548 1.6449 1.7507 1.8808.0537.363 0.9 p 0.000 0.001 0.00 0.003 0.004 0.005 0.006 0.007 0.008 0.009 p 0.95 1.6449 1.6546 1.6646 1.6747 1.6849 1.6954 1.7060 1.7169 1.779 1.739 0.95 0.96 1.7507 1.764 1.7744 1.7866 1.7991 1.8119 1.850 1.8384 1.85 1.8663 0.96 0.97 1.8808 1.8957 1.9110 1.968 1.9431 1.9600 1.9774 1.9954.0141.0335 0.97 0.98.0537.0749.0969.101.1444.1701.1973.6.571.904 0.98 0.99.363.3656.4089.4573.511.5758.651.7478.878 3.090 0.99 18 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

Table 5: Percetage Poits of the Studet s t-distributio The table gives the values of satisfyig P(X ) = p, where X is a radom variable havig the Studet s t-distributio with ν degrees of freedom. p 0.9 0.95 0.975 0.99 0.995 p 0.9 0.95 0.975 0.99 0.995 ν ν 1 3.078 6.314 1.706 31.81 63.657 9 1.311 1.699.045.46.756 1.886.90 4.303 6.965 9.95 30 1.310 1.697.04.457.750 3 1.638.353 3.18 4.541 5.841 31 1.309 1.696.040.453.744 4 1.533.13.776 3.747 4.604 3 1.309 1.694.037.449.738 5 1.476.015.571 3.365 4.03 33 1.308 1.69.035.445.733 6 1.440 1.943.447 3.143 3.707 34 1.307 1.691.03.441.78 7 1.415 1.895.365.998 3.499 35 1.306 1.690.030.438.74 8 1.397 1.860.306.896 3.355 36 1.306 1.688.08.434.719 9 1.383 1.833.6.81 3.50 37 1.305 1.687.06.431.715 10 1.37 1.81.8.764 3.169 38 1.304 1.686.04.49.71 11 1.363 1.796.01.718 3.106 39 1.304 1.685.03.46.708 1 1.356 1.78.179.681 3.055 40 1.303 1.684.01.43.704 13 1.350 1.771.160.650 3.01 45 1.301 1.679.014.41.690 14 1.345 1.761.145.64.977 50 1.99 1.676.009.403.678 15 1.341 1.753.131.60.947 55 1.97 1.673.004.396.668 16 1.337 1.746.11.583.91 60 1.96 1.671.000.390.660 17 1.333 1.740.110.567.898 65 1.95 1.669 1.997.385.654 18 1.330 1.734.101.55.878 70 1.94 1.667 1.994.381.648 19 1.38 1.79.093.539.861 75 1.93 1.665 1.99.377.643 0 1.35 1.75.086.58.845 80 1.9 1.664 1.990.374.639 1 1.33 1.71.080.518.831 85 1.9 1.663 1.998.371.635 1.31 1.717.074.508.819 90 1.91 1.66 1.987.368.63 3 1.319 1.714.069.500.807 95 1.91 1.661 1.985.366.69 4 1.318 1.711.064.49.797 100 1.90 1.660 1.984.364.66 5 1.316 1.708.060.485.787 15 1.88 1.657 1.979.357.616 6 1.315 1.706.056.479.779 150 1.87 1.655 1.976.351.609 7 1.314 1.703.05.473.771 00 1.86 1.653 1.97.345.601 8 1.313 1.701.048.467.763 1.8 1.645 1.960.36.576 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 19

Table 6: Percetage Poits of the χ Distributio The table gives the values of satisfyig P(X ) = p, where X is a radom variable havig the χ distributio with ν degrees of freedom. p 0.005 0.01 0.05 0.05 0.1 0.9 0.95 0.975 0.99 0.995 p ν ν 1 0.00004 0.000 0.001 0.004 0.016.706 3.841 5.04 6.635 7.879 1 0.010 0.00 0.051 0.103 0.11 4.605 5.991 7.378 9.10 10.597 3 0.07 0.115 0.16 0.35 0.584 6.51 7.815 9.348 11.345 1.838 3 4 0.07 0.97 0.484 0.711 1.064 7.779 9.488 11.143 13.77 14.860 4 5 0.41 0.554 0.831 1.145 1.610 9.36 11.070 1.833 15.086 16.750 5 6 0.676 0.87 1.37 1.635.04 10.645 1.59 14.449 16.81 18.548 6 7 0.989 1.39 1.690.167.833 1.017 14.067 16.013 18.475 0.78 7 8 1.344 1.646.180.733 3.490 13.36 15.507 17.535 0.090 1.955 8 9 1.735.088.700 3.35 4.168 14.684 16.919 19.03 1.666 3.589 9 10.156.558 3.47 3.940 4.865 15.987 18.307 0.483 3.09 5.188 10 11.603 3.053 3.816 4.575 5.578 17.75 19.675 1.90 4.75 6.757 11 1 3.074 3.571 4.404 5.6 6.304 18.549 1.06 3.337 6.17 8.300 1 13 3.565 4.107 5.009 5.89 7.04 19.81.36 4.736 7.688 9.819 13 14 4.075 4.660 5.69 6.571 7.790 1.064 3.685 6.119 9.141 31.319 14 15 4.601 5.9 6.6 7.61 8.547.307 4.996 7.488 30.578 3.801 15 16 5.14 5.81 6.908 7.96 9.31 3.54 6.96 8.845 3.000 34.67 16 17 5.697 6.408 7.564 8.67 10.085 4.769 7.587 30.191 33.409 35.718 17 18 6.65 7.015 8.31 9.390 10.865 5.989 8.869 31.56 34.805 37.156 18 19 6.844 7.633 8.907 10.117 11.651 7.04 30.144 3.85 36.191 38.58 19 0 7.434 8.60 9.591 10.851 1.443 8.41 31.410 34.170 37.566 39.997 0 1 8.034 8.897 10.83 11.591 13.40 9.615 3.671 35.479 38.93 41.401 1 8.643 9.54 10.98 1.338 14.041 30.813 33.94 36.781 40.89 4.796 3 9.60 10.196 11.689 13.091 14.848 3.007 35.17 38.076 41.638 44.181 3 4 9.886 10.856 1.401 13.848 15.659 33.196 36.415 39.364 4.980 45.559 4 5 10.50 11.54 13.10 14.611 16.473 34.38 37.65 40.646 44.314 46.98 5 6 11.160 1.198 13.844 15.379 17.9 35.563 38.885 41.93 45.64 48.90 6 7 11.808 1.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49.645 7 8 1.461 13.565 15.308 16.98 18.939 37.916 41.337 44.461 48.78 50.993 8 9 13.11 14.56 16.047 17.708 19.768 39.087 4.557 45.7 49.588 5.336 9 30 13.787 14.953 16.791 18.493 0.599 40.56 43.773 46.979 50.89 53.67 30 31 14.458 15.655 17.539 19.81 1.434 41.4 44.985 48.3 5.191 55.003 31 3 15.134 16.36 18.91 0.07.71 4.585 46.194 49.480 53.486 56.38 3 33 15.815 17.074 19.047 0.867 3.110 43.745 47.400 50.75 54.776 57.648 33 34 16.501 17.789 19.806 1.664 3.95 44.903 48.60 51.996 56.061 58.964 34 35 17.19 18.509 0.569.465 4.797 46.059 49.80 53.03 57.34 60.75 35 36 17.887 19.3 1.336 3.69 5.643 47.1 50.998 54.437 58.619 61.581 36 37 18.586 19.960.106 4.075 6.49 48.363 5.19 55.668 59.89 6.883 37 38 19.89 0.691.878 4.884 7.343 49.513 53.384 56.896 61.16 64.181 38 39 19.996 1.46 3.654 5.695 8.196 50.660 54.57 58.10 6.48 65.476 39 40 0.707.164 4.433 6.509 9.051 51.805 55.758 59.34 63.691 66.766 40 45 4.311 5.901 8.366 30.61 33.350 57.505 61.656 65.410 69.957 73.166 45 50 7.991 9.707 3.357 34.764 37.689 63.167 67.505 71.40 76.154 79.490 50 55 31.735 33.570 36.398 38.958 4.060 68.796 73.311 77.380 8.9 85.749 55 60 35.534 37.485 40.48 43.188 46.459 74.397 79.08 83.98 88.379 91.95 60 65 39.383 41.444 44.603 47.450 50.883 79.973 84.81 89.177 94.4 98.105 65 70 43.75 45.44 48.758 51.739 55.39 85.57 90.531 95.03 100.45 104.15 70 75 47.06 49.475 5.94 56.054 59.795 91.061 96.17 100.839 106.393 110.86 75 80 51.17 53.540 57.153 60.391 64.78 96.578 101.879 106.69 11.39 116.31 80 85 55.170 57.634 61.389 64.749 68.777 10.079 107.5 11.393 118.36 1.35 85 90 59.196 61.754 65.647 69.16 73.91 107.565 113.145 118.136 14.116 18.99 90 95 63.50 65.898 69.95 73.50 77.818 113.038 118.75 13.858 19.973 134.47 95 100 67.38 70.065 74. 77.99 8.358 118.498 14.34 19.561 135.807 140.169 100 0 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017

Table 7: Percetage Poits of the F-distributio The tables give the values of satisfyig P(X ) = p, where X is a radom variable havig the F-distributio with ν 1 degrees of freedom i the umerator ad ν degrees of freedom i the deomiator. F-distributio ( p = 0.995) Use for oe-tail tests at sigificace level 0.5% or two-tail tests at sigificace level 1%. ν 1 1 3 4 5 6 7 8 9 10 11 1 15 0 5 30 40 50 100 ν 1 ν ν 1 1611 0000 1615 500 3056 3437 3715 395 4091 44 4334 446 4630 4836 4960 5044 5148 511 5337 5464 1 198.5 199.0 199. 199. 199.3 199.3 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.5 199.5 199.5 199.5 199.5 199.5 3 55.55 49.80 47.47 46.19 45.39 44.84 44.43 44.13 43.88 43.69 43.5 43.39 43.08 4.78 4.59 4.47 4.31 4.1 4.0 41.83 3 4 31.33 6.8 4.6 3.15.46 1.97 1.6 1.35 1.14 0.97 0.8 0.70 0.44 0.17 0.00 19.89 19.75 19.67 19.50 19.3 4 5.78 18.31 16.53 15.56 14.94 14.51 14.0 13.96 13.77 13.6 13.49 13.38 13.15 1.90 1.76 1.66 1.53 1.45 1.30 1.14 5 6 18.635 14.544 1.917 1.08 11.464 11.073 10.786 10.566 10.391 10.50 10.133 10.034 9.814 9.589 9.451 9.358 9.41 9.170 9.06 8.879 6 7 16.36 1.404 10.88 10.050 9.5 9.155 8.885 8.678 8.514 8.380 8.70 8.176 7.968 7.754 7.63 7.534 7.4 7.354 7.17 7.076 7 8 14.688 11.04 9.596 8.805 8.30 7.95 7.694 7.496 7.339 7.11 7.104 7.015 6.814 6.608 6.48 6.396 6.88 6. 6.088 5.951 8 9 13.614 10.107 8.717 7.956 7.471 7.134 6.885 6.693 6.541 6.417 6.314 6.7 6.03 5.83 5.708 5.65 5.519 5.454 5.3 5.188 9 10 1.86 9.47 8.081 7.343 6.87 6.545 6.30 6.116 5.968 5.847 5.746 5.661 5.471 5.74 5.153 5.071 4.966 4.90 4.77 4.639 10 11 1.6 8.91 7.600 6.881 6.4 6.10 5.865 5.68 5.537 5.418 5.30 5.36 5.049 4.855 4.736 4.654 4.551 4.488 4.359 4.6 11 1 11.754 8.510 7.6 6.51 6.071 5.757 5.55 5.345 5.0 5.085 4.988 4.906 4.71 4.530 4.41 4.331 4.8 4.165 4.037 3.904 1 13 11.374 8.186 6.96 6.33 5.791 5.48 5.53 5.076 4.935 4.80 4.74 4.643 4.460 4.70 4.153 4.073 3.970 3.908 3.780 3.647 13 14 11.060 7.9 6.680 5.998 5.56 5.57 5.031 4.857 4.717 4.603 4.508 4.48 4.47 4.059 3.94 3.86 3.760 3.697 3.569 3.436 14 15 10.798 7.701 6.476 5.803 5.37 5.071 4.847 4.674 4.536 4.44 4.39 4.50 4.070 3.883 3.766 3.687 3.585 3.53 3.394 3.60 15 0 9.944 6.986 5.818 5.174 4.76 4.47 4.57 4.090 3.956 3.847 3.756 3.678 3.50 3.318 3.03 3.13 3.0.959.88.690 0 5 9.475 6.598 5.46 4.835 4.433 4.150 3.939 3.776 3.645 3.537 3.447 3.370 3.196 3.013.898.819.716.65.519.377 5 30 9.180 6.355 5.39 4.63 4.8 3.949 3.74 3.580 3.450 3.344 3.55 3.179 3.006.83.708.68.54.459.33.176 30 40 8.88 6.066 4.976 4.374 3.986 3.713 3.509 3.350 3. 3.117 3.08.953.781.598.48.401.96.30.088 1.93 40 50 8.66 5.90 4.86 4.3 3.849 3.579 3.376 3.19 3.09.988.900.85.653.470.353.7.164.097 1.951 1.786 50 100 8.41 5.589 4.54 3.963 3.589 3.35 3.17.97.847.744.657.583.411.7.108.04 1.91 1.840 1.681 1.485 100 7.879 5.98 4.79 3.715 3.350 3.091.897.744.61.519.43.358.187.000 1.877 1.789 1.669 1.590 1.40 1.001 F-distributio ( p = 0.99) Use for oe-tail tests at sigificace level 1% or two-tail tests at sigificace level %. ν 1 1 3 4 5 6 7 8 9 10 11 1 15 0 5 30 40 50 100 ν 1 ν ν 1 405 5000 5403 565 5764 5859 598 5981 60 6056 6083 6106 6157 609 640 661 687 6303 6334 6366 1 98.50 99.00 99.17 99.5 99.30 99.33 99.36 99.37 99.39 99.40 99.41 99.4 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50 3 34.1 30.8 9.46 8.71 8.4 7.91 7.67 7.49 7.35 7.3 7.13 7.05 6.87 6.69 6.58 6.50 6.41 6.35 6.4 6.13 3 4 1.0 18.00 16.69 15.98 15.5 15.1 14.98 14.80 14.66 14.55 14.45 14.37 14.0 14.0 13.91 13.84 13.75 13.69 13.58 13.46 4 5 16.6 13.7 1.06 11.39 10.97 10.67 10.46 10.9 10.16 10.05 9.96 9.89 9.7 9.55 9.45 9.38 9.9 9.4 9.13 9.0 5 6 13.745 10.95 9.780 9.148 8.746 8.466 8.60 8.10 7.976 7.874 7.790 7.718 7.559 7.396 7.96 7.9 7.143 7.091 6.987 6.880 6 7 1.46 9.547 8.451 7.847 7.460 7.191 6.993 6.840 6.719 6.60 6.538 6.469 6.314 6.155 6.058 5.99 5.908 5.858 5.755 5.650 7 8 11.59 8.649 7.591 7.006 6.63 6.371 6.178 6.09 5.911 5.814 5.734 5.667 5.515 5.359 5.63 5.198 5.116 5.065 4.963 4.859 8 9 10.561 8.0 6.99 6.4 6.057 5.80 5.613 5.467 5.351 5.57 5.178 5.111 4.96 4.808 4.713 4.649 4.567 4.517 4.415 4.311 9 10 10.044 7.559 6.55 5.994 5.636 5.386 5.00 5.057 4.94 4.849 4.77 4.706 4.558 4.405 4.311 4.47 4.165 4.115 4.014 3.909 10 11 9.646 7.06 6.17 5.668 5.316 5.069 4.886 4.744 4.63 4.539 4.46 4.397 4.51 4.099 4.005 3.941 3.860 3.810 3.708 3.60 11 1 9.330 6.97 5.953 5.41 5.064 4.81 4.640 4.499 4.388 4.96 4.0 4.155 4.010 3.858 3.765 3.701 3.619 3.569 3.467 3.361 1 13 9.074 6.701 5.739 5.05 4.86 4.60 4.441 4.30 4.191 4.100 4.05 3.960 3.815 3.665 3.571 3.507 3.45 3.375 3.7 3.165 13 14 8.86 6.515 5.564 5.035 4.695 4.456 4.78 4.140 4.030 3.939 3.864 3.800 3.656 3.505 3.41 3.348 3.66 3.15 3.11 3.004 14 15 8.683 6.359 5.417 4.893 4.556 4.318 4.14 4.004 3.895 3.805 3.730 3.666 3.5 3.37 3.78 3.14 3.13 3.081.977.868 15 0 8.096 5.849 4.938 4.431 4.103 3.871 3.699 3.564 3.457 3.368 3.94 3.31 3.088.938.843.778.695.643.535.41 0 5 7.770 5.568 4.675 4.177 3.855 3.67 3.457 3.34 3.17 3.19 3.056.993.850.699.604.538.453.400.89.169 5 30 7.56 5.390 4.510 4.018 3.699 3.473 3.304 3.173 3.067.979.906.843.700.549.453.386.99.45.131.006 30 40 7.314 5.179 4.313 3.88 3.514 3.91 3.14.993.888.801.77.665.5.369.71.03.114.058 1.938 1.805 40 50 7.171 5.057 4.199 3.70 3.408 3.186 3.00.890.785.698.65.56.419.65.167.098.007 1.949 1.85 1.683 50 100 6.895 4.84 3.984 3.513 3.06.988.83.694.590.503.430.368.3.067 1.965 1.893 1.797 1.735 1.598 1.47 100 6.635 4.605 3.78 3.319 3.017.80.639.511.407.31.48.185.039 1.878 1.773 1.696 1.59 1.53 1.358 1.000 Pearso Edecel Level 3 Advaced Subsidiary ad Advaced GCE i Statistics Statistical Formulae ad Tables Issue 1 August 017 Pearso Educatio Limited 017 1