formula stat

7/30/2019 Formula Stat

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Code No. : MTE 3105LrsT oF FORMULAE rN STATTSTTCS (MTE 3105)

PROBABILITY(1) GeneralAdditionRule

P (A v B) = P (A) + P (B)- P (A n B)General Multiplication RuleP(AnB)=P(A)'P(B)

SAMPLING AND ESTIMATION THEORY(1) Standard error of the means (Samples drawn from a finitepopulation)o- =(Whereo; Standard deviation of the sampling distribution of the meanso Standard deviation of the populationN Population sizen Sample sizeStandard error of the means (Samples drawn from a infinitepopulation)

oo;= rNNTransformation to z-score--x-ltoWhereZ standardized scoreX value of variablep the mean of distributiono standard deviation of the distribution

(2t

(3)

N -nN-1


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Gode No. : MTE 3105(4) The confidence limit of the mean of sample from finite population

- zo lw-n-+ t^L -^t"1" \,1/ - 1(5) The confidence limit of the mean of sample infinite population

zoy * ------"lnThe confidence limit of the mean value of the population ( pl.F; L z,o,WhereIt; Mean of sampling distribution of meanszc Confidence coefficient / confidence levelo; Standard error of the meansThe confidence limits of the standard deviation of the populations*zo-xWheres Standard deviation of a sampleThe confidence limits of the mean value of the population (basedon small sample size)

tsvI cAL"ln -l

Wheretc confidence coefficient of small sample sizes standard deviation of a samplen sample size

(6)

(71

(8)


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Code No. : MTE 3105CHI-SQUARE HYPOTHESIS TEST(1) When expected frequencies are eggi[

nL- kWheren Sum of all observed frequenciesk Number of categories

(21 When expected frequencies are not all equal-E=hpWheren Sum of all observed frequenciesp Probability for the category

(3) Ghi-Square Test Statistic,, -rlio-D'l1' ul E -J

WhereO Observed frequenciesE Expected frequencies

ANALYSTS OF VARTANCE (ANOVA)(1) Test Statistic for One-Way ANOVA (Calculations with Equal

Sample Sizes)- _ variancebetween samplesL= variance within samplesWhereVariance between samples =nsx2{sx2 variance of sampte means)Variance within samples = sp' (sp' pooled variance or the meanof the sample variances)


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Code No. : MTE 3105(21 Test Statistic for One-Way ANOVA (Calculations with UnequalSample Sizes)

- _ variancebetween samplesL-variance within samplesr-llZ',@,-')'Ilfrrlr= L J' I >,


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Code No. : MTE 3105LINEAR REGRESSION(1) Prediction of equation in linear regression

V=bo+brxwhere

br=

and bo=i-b,iCoefficient of determination R2

HYPOTHESIS TESTING(1) Testing claims about a population standard deviation or variance

-, - (r- l)t'^- o'Wheren^ sample sizes' sample varianceo2 population variance (given in null hypothesis)l2l Testing claims about population mean based on small sampleusing Student t-distribution

Testing claims about population mean based on big sample usingstandard Normal distributionx- u-t-

x- u-xt-4nl=

(3)

ot-4n

Z*'-(I')' Zv'- (Iv)'

Z*'-(I")' Zv'-(Iv)'


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(4) Testing a claim about a population proportion== F- Plpq!;Wheren number of trialsi, Ilsampleproportion)np population proportion (used in the null hyppthesis)q 1-p

19


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Code No. : MTE 3105Standard Normal Distribution Table

source:spiegel, M.R. and stephens, 1.J., sfafisfics 13'd Edition;, Appendix ll, The McGraw-Hill Companies, lnc., Singapore.

0.00,t0,tU.J0.4

0sa.i0.80't1.0Llt.:,.31.4r,9!.61.7i.81.9

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,om0 ,ol{0,039t .043$.07t3 .0$a,, t?9 .l2l?.15t4 ,1591.tfls "l$50.?:5$ .?2qt.35s0 :61238St "t9r$,3t59 .!r8r.3413 .3+rt.3543 "tt6!,.3$49 -3*69.4031 .40{9.,1i9? .eiol.4j3? ,43dt.44f2 4463.4t5,{ _4564.4ir4l .d$49,4?13 .4? I 0',47i4 "4V18.4$?1 .{g2S.48it "'1S61.4893 .489d.4il8 -4920.4938 .4940.dgtx _495t"4965 .4966,,19?4 ,49?5.4981 ,Ca&3"'4?8? .49*7-4990 {9.1t"4993 .49.e.1,{rp5 ,{9$5.49q?. 4917.dtgfl 49ns.,1998 .4t98-49$9 .4199;499* .{99t.J$rr. .Jmo

.sryo .ot?q"04?s .Sfi?"os?f [email protected]?t5 .t:93.t6*E "t&4,rst5 ,3it9..2$4 .t137-t6il? .2673.2939 .Wi.3tt2 .31:3,,3461 :148i.36*6 .3?09.i$&$ .3t0td0{6 .i0s3.*2t? :rli36,{557 ,4}?U.44?1 .c4*4.45?t .4iS2.C656 146&9.4n6 .4732.rd?El .4?E.8',{J}} .tl!t4.ds6t ,4$il.4*S8 .dgQl.49i2 .49:5"49{l i..943.il9t6 .49i?.496? .dtl68.49?6 .getl:i1982 ;497t.{t8? .4e$l,4t)91 .4991.4194. .4{qt.{tgt ,4y*6j491? .$!

iqt6B.0537.w{8,ltll..1700.10J4 _iltg9.3?04.2W"t164.35$$.t?19.19r5.4099.$?$t,{tJ*l.4495.4591"467 rr47]S,d?93,4838.4$?5,4904.4927,{945.4959"4969,49',17.498{"4988:4W7

&149 .Q139;0596 .0$.16,.F 87 .t0a{.136[ -t406,t136 .t?.?esass J!2s.34$ "7+r{.??34 .rl6f,10?t .30f1.&s9 ,31t5.lml i5s4.3?4$ .3fl0.19&t .3$dl:.lill5 .4131.43S5 ,4219,,{394 ,440i.{t05 .4:1545i9: ,.{60s;d6?8 .468d,4744 "{75b.4WS .4805.{84: .{846.{8?8 .4s$t.d905 ,4qts,4t?9 *Ett

.,ts18

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,ot?f .01t$ .pj3e,0f?5 fr:n4 ,0?5$,1064 .il03 "il{r"r{4t ,t48d .t5l?.rt08 .t844 ..1819,?f t? .2110 ,?224.:'l*{ .2518 .t$4t^x?94 ,2$:3 .2*52"107f .it06 .313'..$40 J365 .3389.3f?? .i59r, "3{2t^3?90 .38t0 .tE30.]s80 .399? .40t5-4t{? .4t62 ,4t71;41$l .,1386 .4119:{4lE .*rt?9 .,1441.d5?J i453t ..1$45,s616 .46!5 ,.1533.4693 ..r69t ..1?06;4756 .4761 .476t.{808 .48t2 .1{t7.48-50 .4854 .{8.t7-t884 "488? .4890.491I .49t3 .49t6.4912 .4974 {gt6.4949 .{9il .'r95?.4{6? .4963 .4964_4912 .4973 .49744979 "4t80 .49Et.,1985 .d986 *9S6.4989 .4S90.4W2 "499t.49tr .4r9t.49$6 ;491$.4*97 ,4 9r

.4946:i1960.4970cgrB.{tt4,dt89.499:.{ 9.{"4.89i6,tf,9?.$9$,;'ryg:4999rd999.s000

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.{rt*"4999.499S.4199.tofit

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.4e9q' .{s98 ,4e98.4999 -{994 .4399.499v ,4999 .d999.4W' ;d999 .4M;rf,00


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Code No. : MTE 3105

Student's f Distribution Tablewith v Degrees of Freedom(shaded area = P)

I,oli 1.9 r$t{, ,.9t f3p l$?o.i5eoI2,t{,5dJ3I

r0ilI3lll4l5l61'|islt2lf1zt24aa26n2Ex9?0h60

t20cto

6:,669,9:5;E4tlr604.033.11IJOl;i6.3;?5

3. l?3:ll3 {J6l0!2.9t1.95, ot2.901.882,81i

2.8{t.8l2.82t.8t?:802.792,r8t.172.767^16

tf

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