A Statistics Summary-sheet
Sampling Conditions Confidence Interval Test Statistic
σ2 is known ⇒
X
∼ N (µ, σ2/n)
±n
ZX
σ
α
2/ n
X
Z/
0
σ
µ
−
=
Yes
σ2 is unknown ⇒
X
∼ N (µ, σ2/n)
±n
s
ZX 2/
α
ns
X
Z/
0
µ
−
=
Is n is large, say over 30?
−
±n
pp
Zp )1(
2/
α
n
pp
pp
Z)1( 00
0
−
−
=
No X ∼ N (µ, σ2) and σ2 is known ⇒
X
∼ N (µ, σ2/n)
±n
ZX
σ
α
2/ n
X
Z/
0
σ
µ
−
=
X ∼ N (µ, σ2) and σ2 is unknown ⇒
X
∼ tn-1 (µ, σ2/n)
±−n
s
tX n2/,1
α
ns
X
tn/
0
1
µ
−
=
−
If n is not large, say over 30 and X is not ∼
∼∼
∼ N (µ
µµ
µ, σ
σσ
σ2), cannot proceed with parametric statistics.
