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ST104a Statistics 1

Examination Formula Sheet

Expected value of a discrete randomvariable:

= E[X] =Ni=1

pixi

Standard deviation of a discrete randomvariable:

=2 =

Ni=1

pi(xi )2

The transformation formula:

Z=X

Finding Zfor the sampling distributionof the sample mean:

Z=X /n

Finding Zfor the sampling distributionof the sample proportion:

Z=

P

(1)

n

Confidence interval endpoints for asingle mean ( known):

xz

n

Confidence interval endpoints for asingle mean ( unknown):

x tn1sn

Confidence interval endpoints for asingle proportion:

p zp(1p)

n

Sample size determination for a mean:

n Z22

e2

Sample size determination for aproportion:

n Z2p(1p)

e2

Z-test of hypothesis for a single mean (known):

Z=X /n

t-test of hypothesis for a single mean (unknown):

t=X S/n

1

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Z-test of hypothesis for a singleproportion:

Z= p (1)n

Z-test for the difference between two means(variances known):

Z= (X1 X2) (1 2)

21n1 +

22

n2

t-test for the difference between two means(variances unknown):

t= (X1 X2) (1 2)

S2p

1n1

+ 1n2

Confidence interval endpoints for thedifference between two means:

(x1 x2) tn1+n22s2p

1

n1+

1

n2

Pooled variance estimator:

S2p =(n1 1)S21+ (n2 1)S22

n1+ n2 2

t-test for the difference in means inpaired samples:

t=Xd dSd/

n

Confidence interval endpoints for thedifference in means in paired samples:

xdtn1

sd

n

Z-test for the difference between twoproportions:

Z= (P1 P2) (1 2)

P(1 P)

1n1

+ 1n2

Pooled proportion estimator:

P =R1+ R2n1+ n2

Confidence interval endpoints for thedifference between two proportions:

(p1 p2) zp1(1p1)

n1+p2(1p2)

n2

2 test of association:

ri=1

cj=1

(Oij Eij)2Eij

Sample correlation coefficient:

r=

ni=1 xiyi nxyn

i=1 x2i nx2

ni=1 y

2i ny2

Spearman rank correlation:

rs = 16n

i=1 d2i

n(n2

1)

Simple linear regression line estimates:

b =

ni=1 xiyi nxy

ni=1 x2i nx2a = y bx

2

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Dennis V. Lindley, William F. Scott, New Cambridge Statistical Tables, (1995) Cambridge University Press, reproduced with permission.