Statistics Formula Sheet

z−confidence interval: x ± 2

αz n

σ

t-confidence interval: x ± 2

αt n

s (d.f. = n – 1)

Confidence interval for proportion: p̂ ± 2

αz n

pp )ˆ1(ˆ −

Confidence interval for difference of two means: 2

22

1

21

2

21 nnzxx

σσα +⋅±−

Confidence interval for difference of two means:

If 22

21 σσ = ,

+⋅

−+−+−⋅±−

2121

222

211

2

21

11

2

)1()1(

nnnn

snsntxx α , d.f. = n1 + n2 − 2

If 22

21 σσ ≠ ,

2

22

1

21

2

21 n

s

n

stxx +⋅±− α , d.f. = min(n1 − 1, n2 − 1)

z-test statistic: n

xz σ

µ0−=

t-test statistics: n

sx

t 0µ−= (d.f. = n – 1)

z-test for proportion: z =

n

pp

pp

)1(

ˆ

00

0

−−

z-test statistic for two means:

2

22

1

21

021

nn

Dxxz

σσ+

−−=

t-test statistic for two means:

If 22

21 σσ = ,

+⋅

−+−+−

−−=

2121

222

211

021

11

2

)1()1(

nnnn

snsn

Dxxt , d.f. = n1 + n2 − 2

If 22

21 σσ ≠ ,

2

22

1

21

021

n

s

n

s

Dxxt

+

−−= , d.f. = min(n1 − 1, n2 − 1) [rough approximate]

Chi-square test Statistics:

χ2 = freq. expected

freq.) expected freq. (observed 2

,

−∑ji

∼ χ2 d.f. = (r-1)(c-1)