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FORMULAS
Sample statistics Sample mean: x=
∑ x i , Sample standard deviation (definition) n
Computational formula s=

s=
 ∑ xi 2
n
n−1

∑  xi −x2 n−1
∑ x 2i −
Population parameters:
Population mean: =
or  =

∑ xi
N
Population standard deviation:  =
2
∑ x i −2

∑  x i−2 N
N
Standard score or z­score z =
x−μ
If x ~ N  ,   then z ~ N 0,1
σ
Probability
P(E)=f/N P(A or B) = P(A) + P(B) ­ P(A and B)
Sampling Distribution of x
x = ,  x =

x
 −
, Standardized version of x : z=
 / n
n
Confidence Intervals for 
Confidence level C= 1−∗100%
2
 


z 
Z­interval: x ±z  /2
Margin of error: E=z  /2
, Sample size estimation: n=  /2
n
n
E
t­interval: x ±t  /2
s
x −
, df=n­1, Studentized version of x : t=
s/  n
n