Formula Card For Weiss'S Elementary Statistics, Fourth Edition Page 3
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3FORMULA CARD FOR WEISS’S ELEMENTARY STATISTICS, FOURTH EDITION
Larry R. Griffey
•
Two-sample z-interval for p
p
•
SSTR + SSE
:
One-way ANOVA identity: SST
1
2
( ˆ p
ˆ p
) ± z
·
ˆ p
(1
ˆ p
)/n
+ ˆ p
(1
ˆ p
)/n
α/2
•
1
2
1
1
1
2
2
2
Computing formulas for sums of squares in one-way ANOVA:
(Assumptions: independent samples; x
, n
x
, x
, n
x
are
1
1
1
2
2
2
x
2
( x)
2
/n
SST
all 5 or greater)
(T
/n
)
( x)
/n
2
2
SSTR
j
j
•
Margin of error for the estimate of p
p
:
1
2
SSE
SST
SSTR
E
z
·
ˆ p
(1
ˆ p
)/n
+ ˆ p
(1
ˆ p
)/n
α/2
1
1
1
2
2
2
•
Mean squares in one-way ANOVA:
•
Sample size for estimating p
p
:
1
2
SSTR
SSE
,
z
2
MSTR
MSE
α/2
k
n
k
n
n
1
0.5
1
2
E
•
or
Test statistic for one-way ANOVA (independent samples, normal
z
2
populations, and equal population standard deviations):
α/2
n
n
ˆ p
(1
ˆ p
) + ˆ p
(1
ˆ p
)
1
2
1g
1g
2g
2g
E
MSTR
F
rounded up to the nearest whole number (g
“educated guess”)
MSE
(k
1, n
k).
with df
CHAPTER 12
Chi-Square Procedures
CHAPTER 14
Inferential Methods in Regression and Correlation
•
Expected frequencies for a chi-square goodness-of-fit test:
E
np
•
Population regression equation: y
β
+ β
x
0
1
•
Test statistic for a chi-square goodness-of-fit test:
SSE
•
Standard error of the estimate: s
e
n
χ
2
(O
E)
2
/E
2
k
1, where k is the number of possible values for the
•
Test statistic for H
: β
with df
0:
0
1
variable under consideration.
b
1
t
√
s
/
S
•
e
xx
Expected frequencies for a chi-square independence test:
n
R · C
with df
2.
E
n
•
Confidence interval for β
:
1
where R
row total and C
column total.
s
e
b
± t
·
√
α/2
1
S
•
xx
Test statistic for a chi-square independence test:
n
χ
(O
E)
/E
with df
2.
2
2
(r
1), where r and c are the number of possible
with df
1)(c
•
Confidence interval for the conditional mean of the response
variable corresponding to x
values for the two variables under consideration.
:
p
(x
x/n)
2
CHAPTER 13
Analysis of Variance (ANOVA)
1
p
ˆ y
± t
· s
+
p
α/2
e
n
S
xx
•
Notation in one-way ANOVA:
n
with df
2.
k
number of populations
n
•
total number of observations
Prediction interval for an observed value of the response variable
corresponding to x
x
mean of all n observations
:
p
n
size of sample from Population j
j
(x
x/n)
2
1
p
ˆ y
± t
· s
1 +
+
x
mean of sample from Population j
p
α/2
e
j
n
S
xx
s
2
variance of sample from Population j
j
n
with df
2.
T
sum of sample data from Population j
j
•
Test statistic for H
: ρ
0:
0
•
Defining formulas for sums of squares in one-way ANOVA:
r
t
(x
x)
2
SST
r
2
1
n
(x
x)
2
n
SSTR
2
j
j
n
(n
2
with df
2.
SSE
1)s
j
j
-3-
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