Final Exam Formulas
Lecture I
w quality
x
∑
∑
Weighted Average
Lectured
DiggerCV
Coefficient of
Variation
riskier
Lectures
f xn10.5 Boxplots
f xn10.5
xn10.5
Probabilities
lecture 4
(
(
more
volatile
)
( )
5 6
)
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( )
(
( | )
( | )
If independent, then (
)
)
( )
(
)
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Final Exam Formulas
( )
Expected Value
( )
( )
∑
6
Lecture
expected
( )
Binomial
µ n.p
lecture't
Poisson
31 14
lectures
(
Exponential
4
same
distribution
ghe
unwhercalculating
subtract
n
whenuisgiverorxisgives
( )
⁄
)
(
Uniform
(
⁄
)
)
Normal
Sample Means
(when
⁄
√
known)
√
√
Confidence Intervals and Finding the Sample Size
√
when
known
√
Population standard deviation
is unknown. Have a sample
standard deviation s (not )
(
)
Always round up to a whole number
Always use Z to find a sample size
(
√
( )
(
)
)
Use = 0.50 if nothing
is known about p
Final Exam Formulas
whennis
given
√
√ (
√
See note above
Chi Square Test for Independence
∑
(
)
(
)
(
)
Linear Regression
̂
t-statistic and p-value provided
in Excel outputs
DecisionRole
RejectHoif teststatistic
DecisionwithJustification
a
Gest 2.890C
crit
RejectHo because teststatis in rejectionzone 3.75
)
Midterm 2 Formulas
√
√
√
(
)
√
)
(
)
√ (
)
( )
√
(
Matched-pair t-test for dependent samples
Lower-tail
Upper-Tail
Two-Tails
d addupalldifferences
n
Sd Sxoncalculator
sample mean difference
sample standard deviation
√
Two Independent Populations
Lower-tail Test
Upper-Tail Test
Pooled
(standard deviations same)
(
)
√
(
(
)
(
(
)
)
)
(
(
Two-Tail Test
Unpooled
(standard deviations different)
(
)
(
)
√
)
)
intervalin
I
Midterm 2 Formulas
Two Proportions:
Lower-tail Test
Upper-Tail Test
Two-Tail Test
value
of
find
onetable
Pvalve
1
TwoTailed2 ZEE
OneTailed CZEFest
Zant
(
)
√ (
(
)(
)
)
Chi Square Test for Independence
∑
(
)
(
)
(
)
Linear Regression
̂
t-statistic and p-value provided
in Excel outputs
ANOVA Test
df: numerator =
Overall mean (grand mean):
Variation Between Groups: SSB
(Sum of Squares Between groups)
Variation Within Each Group: SSW
(Sum of Squares Within the groups)
̿
∑
denominator =
∑
∑
(
∑ ∑(
̿)
)
̿
n = total number of values