Test Statistic Excel functions Confidence Interval formula
One population mean
sigma known
H0: = value
H1: ><≠ value
z =
x -
s / n
=NORM.S.DIST( ) X± Za/2sn=NORM.S.INV(a/2)
One population mean
sigma unknown
H0: = value
H1: ><≠ value
t =
x -
s/ n
=T.DIST( )
=T.DIST.RT( ) =T.DIST.2T( )
(n-1) degrees of freedom
X± ta/2s
n= T.INV.2T(an-1)
One population
proportions
H0: p = value
H1: p ><≠ value
p(1 p)/n
pˆ p
z
–
–
=
=NORM.S.DIST( )
(n*p and n*(1-p) are
greater than 5)
?̂± ?ఈ/ଶඨ
?̂(1 − ?̂)
?
=NORM.S.INV(a/2)
CHI-SQUARED TESTS
Test statistic: ?
ଶ = ∑
(௦௩ௗି௫ )
మ
௫௧ௗ
; Expected value: ? =
( row total)( column total)
Total sample size
Degrees of freedom goodness of fit: (rows–1); Degrees of freedom independence: (rows-1)*(columns-1)
ANOVA
Source of Variation Sum of
Squares
Degrees of
Freedom
Mean Squares F-statistic
Factor (between) SSB k-1 MSB=SSB/(k-1) F=MSB/MSW
Error (within) SSW n-k MSW=SSW/(n-k)
Total SST n-1
Source of Variation Sum of
Squares
Degrees of
Freedom
Mean Squares F-statistic
Factor A SSA a-1 MSA=SSA/(a-1) F=MSA/MSW
Factor B SSB b-1 MSB=SSB/(b-1) F=MSB/MSW
Interaction SSAB (a-1)*(b-1) MSAB=SSAB/(a-1)*(b-1) F=MSAB/MSW
Error (Within) SSW n-(a*b) MSW=SSW/(n-(a*b))
Total SST n-1
REGRESSION
?
ଶ =
ௌௌோ
ௌௌ்
Prediction Interval:
DESCRIPTIVE:
Mean: ?̅=
∑ ௫
సభ
Variance: ?
ଶ =
∑ (௫ି௫̅)
మ
సభ
ିଵ
