Statistical Formulas
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PA551 Professor Stipak
Statistical Formulas for PA551 Descriptive Statistics: X=
ΣX n
σ 2 =
X=
Σ(X - µ ) n
ΣfX n
2
2
s =
Σ(X - X ) n-1
s=
s
2
2
σ = σ2
Normal Probability Problems: X -µ
z=
X = µ+ zσ
σ
Statistical Inference: z=
t=
z=
X -µ
σX =
σx
X -µ ˆX σ
ˆX= σ
Pˆ - P
σ Pˆ =
σ Pˆ
σ
For mean problems, large n or σ known
n
s n
df = n - 1
P(1 - P) n
For mean problems, σ not known, n small
For proportion problems
Required Sample Size: Letting E be the allowable error for the 95% confidence interval:
n=
3.84 P (1 - P) E
2
n=
3.84 σ 2 2 E
Statistical Formulas for PA551 Descriptive Statistics: X=
ΣX n
σ 2 =
X=
Σ(X - µ ) n
ΣfX n
2
2
s =
Σ(X - X ) n-1
s=
s
2
2
σ = σ2
Normal Probability Problems: X -µ
z=
X = µ+ zσ
σ
Statistical Inference: z=
t=
z=
X -µ
σX =
σx
X -µ ˆX σ
ˆX= σ
Pˆ - P
σ Pˆ =
σ Pˆ
σ
For mean problems, large n or σ known
n
s n
df = n - 1
P(1 - P) n
For mean problems, σ not known, n small
For proportion problems
Required Sample Size: Letting E be the allowable error for the 95% confidence interval:
n=
3.84 P (1 - P) E
2
n=
3.84 σ 2 2 E
