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1 r r Table 4 Biomial Probability Distributio C, r p q This table shows the probability of r successes i idepedet trials, each with probability of success p. p r ;
2 Table 4 cotiued p r :
3 Table 4 cotiued p r
4 Table 4 cotiued p r
5 Table 5 Areas of a Stadard Normal Distributio The table etries represet the area uder the stadard ormal curve from 0 to the specified value of z. z : : For values of z greater tha or equal to 3.70, use 0 to approximate the shaded area uder the stadard ormal curve.
6 Table 6 Studet s t Distributio Studet s t values geerated by Miitab Versio 9. c a a d.f c is a cofidece level: a is the level of sigificace for a oe-tailed test: a is the level of sigificace for a two-tailed test cc
7 Areas of a Stadard Normal Distributio The table etries represet the area uder the stadard ormal curve from 0 to the specified value of z. z : : For values of z greater tha or equal to 3.70, use 0 to approximate the shaded area uder the stadard ormal curve.
8 Some Levels of Cofidece ad Their Correspodig Critical Values Commoly Used Critical Values z 0 from the Stadard Normal Distributio Level of Cofidece c Critical Value z c Type of Test Level of Sigificace Left-tailed Right-tailed Two-tailed ±1.96 ± Table 8 Critical Values of Pearso Product-Momet Correlatio Coefficiet, r a =0.01 a = 0.05 oe tail two tails oe tail two tails For a right-tailed test, use a positive r value: For a left-tailed test, use a egative r value: For a two-tailed test, use a positive r value ad egative r value:
9 Frequetly Used Formulas = sample size N = populatio size f = frequecy Chapter 1 high low Class Width = (icrease to ext umber of classes iteger) upperlimit + lowerlimit Class Midpoit = Lower boudary = lower boudary of previous class + class width Chapter Sample mea X = x x Populatio mea µ = N Rage = largest data value - smallest data value Sample stadard deviatios s = Computatio formula s = SS x = x ( x) SS x 1 Populatio stadard deviatio σ = Sample variace s Populatio variace o (x x) 1 where ( x µ ) s Sample Coefficiet of Variatio CV = 100 x Sample mea for grouped data x = xf Sample stadard deviatio for grouped data s = Chapter 3 ( x x) f 1 Regressio ad Correlatio I all these formulas ( x) SS x = x ( y ) SS y = y SS xy = xy ( x)( y ) N Least squares lie y = a + bx where b = SS xy ad SS x a = y bx Pearso product-momet correlatio coefficiet r = SS xy SS x SS y Coefficiet of determiatio Chapter 4 = r Probability of the complemet of evet A P ot A = 1 P A ( ) ( ) Multiplicatio rule for idepedet evets P A ad B = P A P B ( ) ( ) ( ) Geeral multiplicatio rules P A ad B = P A P B, give ( ) ( ) ( A) ( A ad B) = P( B) P( A give B) P, Additio rule for mutually exclusive evets P A or B = P A + P B ( ) ( ) ( ) Geeral additio rule P A or B = P A + P B ( ) ( ) ( ) P( A ad B) Permutatio rule P,r! = ( r )!! Combiatio rule C,r = r! ( r )! Chapter 5 Mea of a discrete probability distributio µ = xp( x) Stadard deviatio of a discrete probability distributio ( x µ ) P( ) σ = x For Biomial Distributios r = umber of successes; p = probability of success; q = 1 p Biomial probability distributio P(r) = r! ( Mea µ = p Stadard deviatio Chapter 6 σ = Raw score x = zσ + µ x µ Stadard score z = σ pq! r r p q r)!
10 Chapter 7 Mea of x distributio µ x = µ Stadard deviatio of x distributio σ x = Stadard score for x Chapter 8 Cofidece Iterval µ whe 30 for ( ) x z σ < µ < x c + for µ ( whe < 30) d.f. = 1 s x t c < µ < x + t z c x µ z = σ for p ( whe p > 5 ad q > 5) pˆ ( 1 pˆ ) pˆ ( 1 pˆ ) c s σ pˆ zc < p < pˆ + zc where pˆ = r/ Sample Size for Estimatig zc σ meas = E proportios zc = p( 1 p) with prelimiary estimate for p E 1 zc = without prelimiary estimate for p 4 E Chapter 9 Sample Test Statistics for Tests of Hypotheses for µ ( whe 30) for ( whe 30) x µ z = σ x µ µ < ; t = with d.f. = 1 pˆ p for p z = where q = 1 p pq Chapter 10 Sample Test Statistics for Tests of Hypothesis for paired differece d t = d µ d with d.f. = 1 s sd differece of meas large sample ( x1 x ) ( µ µ ) 1 z = σ1 σ = 1 σ differece of proportios pˆ 1 pˆ r 1 + r z = where pˆ = ; qˆ = 1 pˆ ; pˆ qˆ pˆ qˆ pˆ = r 1 1; pˆ r = 1 Cofidece Itervals for differece of meas (whe 1 30 ad 30 ) σ σ x x z 1 x x 1 ( 1 ) + < µ µ < ( 1 ) σ 1 σ + z + 1 for differece of proportios where pˆ = r 1 pˆ = r qˆ = 1 pˆ ; qˆ = pˆ ; pˆ qˆ pˆ qˆ pˆ z ( pˆ ) + < pˆ pˆ < ( pˆ pˆ ) + zc pˆ qˆ Chapter 11 ( O E) x = where E row total colum E = sample size pˆ qˆ ( )( total ) Tests of idepedece d. f. = ( R 1)( C 1) Goodess of fit d. f. = ( umber of etries) 1 Sample test statistic for H 0 : σ = k; d.f. = 1 ( 1) s x = σ Liear Regressio Stadard error or estimate Se = SSxy where b = SSy Cofidece iterval for y y SS y bss E < y E where y p is the predicted y value p p + for x ad ( x x ) 1 E = t c Se 1+ + with d. f. = SS x xy
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