stat

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 /2

s n

=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 /2

s

n

= T.INV.2T(an-1)

One population proportions H0: p= value H1: p ><≠ value

n/)p1(p

pp̂ z

- -

= =NORM.S.DIST( ) (n*p and n*(1-p) are greater than 5)

�̂� ± 𝑍 /

�̂�(1 − �̂�)

𝑛

=NORM.S.INV(a/2)

CHI-SQUARED TESTS

Test statistic: 𝜒 = ∑ ( )

; Expected value: 𝑒 = ( 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

𝑅 = Prediction Interval:

DESCRIPTIVE:

Mean: �̅� = ∑

Variance: 𝑠 = ∑ ( ̅)