Business Statistics Midterm Cheat Sheet

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CI for pop mean:
x±z*(σn)
n=(z*σME)2
Reduce ME
1. Lower confidence
2. reduce σ
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3. increase n
HT for pop mean
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z=x-μσ√n
Errors
I=P(reject H0/H0 true)=α
II=P(accept H0/H0 wrong)
Power=1-β
Increase pow
1. increase α
2. consider alternative µ that is farther than hypothesized µ 3.increase n
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4.decrease σ
One sample t CI
x±t*s√n
One sample t-test
T=x-µ0s√n
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Df=n-1
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P is 2 closest
Two pop means (before and after)
xD±t*sD√nD
xD=x1-x2
sD=x2-(x)2nn-1

Hypothesis test
H0:µa=µb
H1: µa≠µb
T=xd-D0Sd√n
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Df=n-1
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P is 2 closest
Two pop means (2 samples one condition)
σ known
CI:
xd±z*σ12n1+σ22n2
Hypothesis test:
H0:µa=µb
H1: µa≠µb
Z=x1-x2-Dσ12n1+σ22n2
s-known
CI:
xd±t*s12n1+s22n2
Hypothesis test:
t=x1-x2-Ds12n1+s22n2
df= lower of (ni-1)

σ unknown (σ1=σ2)
CI:
xd±t*sp21n1+1n2
sp2=sampled pool variance
df=n1+n2-2
Hypothesis test:
T=x1-x2sp21n1+1n2
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sp2=n1-1s12+n2-1s22n1+n2-2
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P is 2 closest
Compare 2 pop variances
Assumptions:
1.2 pops are normally dist
2. samples are random and indep

H0:σ12=σ12
H1: σ12≠σ12
F=s22s12
(or f=s12s22 when H1:σ12>σ22)
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f: numerator degrees of freedom and denominator degrees of freedom (n-1) Single proportion
p=sample prop=X/n
(X= number of success)
p0=pop prop= S/n
CI:
p±z*p(1-p)n
Hypothesis test
H0:p=p0
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Z=p-p0p(1-p)n
Two pop proportions
CI:
p1-p2±z*p1(1-p1)n1+p2(1-p2)n2
Hypothesis test:
H0:p1=p2
Z=p1-p2p(1-p)(1n1+1n2)
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p=x1+x2n1+n2
Chi-square (indep test)
Hypothesis test:
H0:no association between row and column variables
X2=o-e2e
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df=(#rows-1)(#col-1)
Least squares regression line
Deviation assumptions:
1. independent
2. normally distributed
3. mean=0
4.SD of s
Inference for regression slope
using sample slope to make inference about pop slope
Assumptions:
1. SRS from pop
2. there is a linear relationship in pop
3.SD of the responses about the population line is the same for all values of the explanatory variables 4. response variables varies normally about the pop regression line. CI for slope(β1):
b1±t*sb1
sb1=sSSxx
SSxx=sum of squares
Prediction interval for individual (wider than confidence for mean) ŷ±t*se1+1n+x-x2SSxx
or
ŷ±t*SEŷ
df=n-2
CI for a mean response:
ŷ±t*se1n+x-x2SSxx
or
ŷ±t*SEµ
Hypothesis test:
H0: b1=0 (model has no predictive value)
-if asking for direct relationship use UTT
t=b1sb1
df=n-2
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P value is 2 closest values
Correlation
Hypothesis test:
H0:p=0
T=rn-21-r2
r=correlation
df=n-2
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P value is 2 closest values
Multiple regression
cond’s for error variable ε
1. the prob of distribution of ε is normal
2. the mean of ε is 0
3. th SD of ε is σε, which is constant for each value of x 4. errors are independent
residuals:
ei=yi-ŷi (how far is your value true value)
hypothesis test for individual variable:
H0:βi=0
t=b1sb1
df=n-k-1
P value is 2 closest values
Hypothesis test for entire model:
H0:β1+β2+…+βk=0
H1: at east one βi≠0
F=MSRMSE
df: numerator=k
denominator=n-k-1
Sε=SSEn-k-1
Sε=standard error of estimate
- if Sε is high then there is a lot of variability
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R2=SSR/SST
ANOVA
Hypothesis:
H0:µ1=µ2=…=µk
H1: at least one µi is different
F=MSTMSE
df:...
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