Download STAT 141 Formula Sheet Range = Max − Min IQR = Q 3 − Q1 Outlier

STAT 141 Formula Sheet
Range = M ax − M in
1
IQR = Q3 − Q1
y < Q1 − 1.5 × IQR or y > Q3 + 1.5 × IQR
qP
P
(y−ȳ)2
y
Sample mean and standard deviation: ȳ = n and s =
n−1
Outlier Rule-of-Thumb:
z-scores: z =
y−µ
σ
Correlation: r =
(model based) and z =
y−ȳ
s
(data based)
P
zx zy
n−1
Least-squares regression line: ŷ = b0 + b1 x where
s
b1 = r sxy and b0 = ȳ − b1 x̄
P (A) = 1 − P (Ac )
P (A or B) = P (A) + P (B) − P (A and B)
P (A and B) = P (A) × P (B | A)
P (B | A) =
P (A and B)
P (A)
If A and B are independent, then P (B | A) = P (B)
P
P
E(X) = µ = x P (x)
V ar(X) = σ 2 = (x − µ)2 P (x)
E(X ± c) = E(X) ± c
V ar(X ± c) = V ar(X)
E(aX) = aE(X)
V ar(aX) = a2 V ar(X)
E(X ± Y ) = E(X) ± E(Y )
If X and Y are independent, then V ar(X ± Y ) = V ar(X) + V ar(y)
q
1
x−1
Geometric model: P (x) = q p
µ = p σ = pq2
Binomial model: P (x) = n Cx px q n−x
Sample proportion: µ(p̂) = p SD(p̂) =
Sample mean: µ(ȳ) = µy SD(ȳ) =
µ = np
p pq
σ=
√
npq
n
√σ
n
Central Limit Theorem: As n grows, the sampling distributions of p̂ and ȳ
approach Normal models with mean and standard deviation given above.
STAT 141 Formula Sheet
2
Inference:
Confidence interval for parameter: statistic ± (critical value) × SE(statistic)
Test statistic =
statistic−parameter
SD(statistic)
Parameter
Statistic
p
p̂
p̂1 − p̂2
µ
ȳ
ȳ1 − ȳ2
µd
d¯
qP
β1
µν
yν
p̂q̂
n
q
p1 q 1
n1
+
q
p2 q 2
n2
p̂1 q̂1
n1
√σ
n
µ1 − µ2
se =
SE(statistic)
q
n
p1 − p2
σ
SD(statistic)
p pq
q
σ12
n1
+
+
p̂2 q̂2
n2
√s
n
q
σ22
n2
s21
n1
+
s22
n2
sd
√
n
σd
√
n
(y−ŷ)2
n−2
√se
sx n−1
b1
ŷν = µ̂ν
ŷν
q
SE 2 (b1 ) · (xν − x̄)2 +
q
SE 2 (b1 ) · (xν − x̄)2 +
For testing H0 : p1 − p2 = 0, substitute the pooled estimate p̂pooled =
for p̂1 and p̂2 in the SE formula.
P (Obs−Exp)2
Chi-square statistic: χ2 =
.
Exp
s2e
n
s2e
n
+ s2e
y1 +y2
n1 +n2