Formulario De Estadistica

Formulas and Tables
for Elementary Statistics, Tenth Edition, by Mario F. Triola Copyright 2006 Pearson Education, Inc.

Ch. 3: Descriptive Statistics
x x s s s Sx n Sf Å Å Å Mean Mean (frequency table) Standard deviation Standard deviation (shortcut) Standard deviation (frequency table)

Ch. 7: Confidence Intervals (one population)
ˆ p E p ˆ p E Proportion ˆˆ pq

Sf . x

where E 5za>2

Å n

S(x 2 x) 2 n21 n(n 2 1)

x2E,m,x1E

n(Sx2 ) 2 (Sx) 2

n3S(f . x2 )4 2 3S(f . x)4 2 n(n 2 1) s2

Mean s where E 5 za>2 (s known ) !n s or E 5 ta>2 (s unknown) !n , s2 , (n 2 1)s2
2 xL

(n 2 1)s2
2 xR

Variance

variance

Ch. 7: Sample Size Determination
3za>24 2 . 0.25 E2 ˆˆ 3za>24 2pq E2 za>2s E Proportion

Ch. 4: Probability
n5 P(A or B) 5 P(A) 1 P(B) if A, B aremutually exclusive P(A or B) 5 P(A) 1 P(B) 2 P(A and B) if A, B are not mutually exclusive P(A and B) 5 P(A) . P(B) if A, B are independent P(A and B) 5 P(A) . P(B 0A) if A, B are dependent P(A) 5 1 2 P(A) Rule of complements n! Permutations (no elements alike) nP 5 r (n 2 r)! n! Permutations (n1 alike, ...) n1! n2! . . . nk! n! Combinations nCr 5 (n 2 r)! r! n5

Ch. 9: Confidence Intervals(two populations)
ˆ ˆ ˆ ˆ (p1 2 p2 ) 2 E , (p1 2 p2 ) , (p1 2 p2 ) 1 E where E 5 za>2 Å n1 ˆ ˆ p1q1 1 ˆ ˆ p2q2 n2 (Indep.)

n 5  B

R

ˆ ˆ Proportion (p and q are known)
2

Mean

Ch. 5: Probability Distributions
x . P(x) Mean (prob. dist.) 2 [ x2 . P(x)] Standard deviation (prob. dist.) n! x . n x .p q Binomial probability P(x) (n x)! x! Mean (binomial) n.p 2 .p.q Variance (binomial) nn.p.q
x

(x1 2 x2 ) 2 E , (m1 2 m2 ) , (x1 2 x2 ) 1 E where E 5 ta>2 s2 s2 1 2 1n 2 Å n1 (df n1 smaller of 1, n2 1)

‹

(s1 and s2 unknown and not assumed equal)
2 2 sp sp E 5 ta>2 1   (df 5 n1 1 n2 2 2) n2 Å n1 (n1 2 1)s2 1 (n2 2 1)s2 1 2 2 sp 5 (n1 2 1) 1 (n2 2 1)

‹

P(x)

.e x!

Standard deviation (binomial) Poisson Distribution where e 2.71828

(s1 and s2 unknown but assumedequal)
2 2 s1 s2 E 5 za>2 1 Å n1 n2

Ch. 6: Normal Distribution
z
x

‹

x s

x

or

x

Standard score

(s1, s2 known) d 2 E , md , d 1 E (Matched Pairs) sd where E 5 ta>2 (df n 1) !n

Central limit theorem n Central limit theorem (Standard error)

x

Copyright 2007 Pearson Education, publishing as Pearson Addison-Wesley.

Formulas and Tables
for Elementary Statistics,Tenth Edition, by Mario F. Triola Copyright 2006 Pearson Education, Inc.

Ch. 8: Test Statistics (one population)
z5 ˆ p2p Å n x2m pq Proportion—one population

Ch. 10: Linear Correlation/Regression
Correlation r 5 b1 5 "n(Sx ) 2 (Sx) 2"n(Sy2 ) 2 (Sy) 2
2

nSxy 2 (Sx) (Sy)

nSxy 2 (Sx) (Sy) n(Sx2 ) 2 (Sx) 2 (Sy) (Sx2 ) 2 (Sx) (Sxy) n(Sx2 ) 2 (Sx) 2 Estimated eq. of regression line

z5t5

s> !n (n 2 1)s2 x2 5 s2

s> !n x2m

Mean—one population ( known) Mean—one population ( unknown) Standard deviation or variance— one population

b0 5 y 2 b1x or b0 5 ˆ y 5 b0 1 b1x r2 5 se 5 ˆ y

explained variation total variation Å ˆ S(y 2 y ) 2 n22 y ˆ y t or E
2se

Ch. 9: Test Statistics (two populations)
z5 ˆ ˆ (p1 2 p2 ) 2 (p1 2 p2 ) pq pq 1 n 2 Å n1 (x1 2 x2 ) 2 (m1 2 m2 )Two proportions

Å

Sy2 2 b0Sy 2 b1Sxy n22

E

Prediction interval 1 1 n n(x 0 n( x 2) x)2 ( x)2

t5

s2 s2 1 2 1 Å n1 n2 Two means—independent; s1 and s2 unknown, and not assumed equal.

df n1

smaller of 1, n2 1

where E

‹
t5

Ch. 12: One-Way Analysis of a Variance
Procedure for testing H0: m1 5 m2 5 m3 5 c 1. Use software or calculator to obtain results. 2. Identifythe P-value. 3. Form conclusion: If P-value a, reject the null hypothesis of equal means. If P a, fail to reject the null hypothesis of equal means.

(x1 2 x2 ) 2 (m1 2 m2 ) Å n1
2 sp

1

2 sp

‹

(df
2 sp 5

n1

n2

2)

‹
z5 t5 F5 s2 1 s2 2 x2 5 g x2 5 g x2 5

n2

(n1 2 1)s2 1 (n2 2 1)s2 1 2 n1 1 n2 2 2

Two means—independent; s1 and s2 unknown, but assumed equal. (x1 2...