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Hypothesis Test Formula for Six Sigma Project.
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HYPOTHESIS TESTING PROCEDURE
STEP 1.
Establish the Hypothesis
a.) Null Hypothesis Ho: =
b.) Alternative HypothesisHa:
STEP 2.
Choose a Significance Level a =
STEP 3.
Plan the Test
a.) Choose the Test Statistic (formula)
b.) Determine the Rejection Region
F
or
c2
Z
or
t
0
0
STEP 4.
Collect data and
Calculate test statistic
DATA BLOCK
STEP 5.
Draw conclusion
STEP 6.
Estimate the parameter of interest
and determine Confidence Interval
Hypothesis Tests
Differences in the Means
-
Tests for One Population
Population Variance (
s
2
)
known?
Test To Use
Formula
Yes
Z
-
Test
Z
x
n
where
x
=
-
m
s
m
s
0
/
:
-
Sample Me
an
-
Standard
Mean
-
Population Standard Deviation
n
-
Sample Size
0
No
t
-
Test
t
x
s
n
where
x
s
=
-
m
m
0
/
:
-
Sample Me
an
-
Standard
Mean
-
Sample Standard Deviation
n
-
Sample Size
0
Differences in the Means
-
Tests for Two Population
s
Paired Data
Population
Variances
known?
Population
Variances
Equal?
Test to
Use
Formula
N/A
N/A
Paired
Sample t
-
Test
t
d
s
n
where
d
s
=
/
:
-
Sample Differences Mean
-
Sample Standard Deviation
n
-
Sample Size
t
x
x
n
n
SS
SS
n
n
where
x
A
B
A
B
A
B
A
B
i
=
-
+
+
+
-
1
1
2
:
-
Sample Me
an
n
-
Sample Si
ze
i
Differences in the Means
-
Tests for Two Populations
Population
Variances
known?
Population
Variances
Equal?
Test to
Use
Formula
Yes
N/A
Two Pop
.
Z
-
Test
For Equal Sample Sizes
Z
x
x
n
where
x
A
B
A
B
i
i
=
-
+
1
2
2
(
)
:
s
s
s
-
Sample Mean
-
Population Standard Deviation
n
-
Sample Size
For Unequal Sample Sizes
Z
x
x
n
n
where
x
A
B
A
A
B
B
i
i
=
-
+
s
s
s
2
2
:
-
Sample Mean
-
Population Standard Deviation
n
-
Sample Size
i
No
Yes
Two
Pop.
,
Pooled
Variance
t
-
Test
For equal sample sizes
t
x
x
s
s
n
where
x
s
A
B
A
B
i
=
-
+
2
2
:
-
Sample Mean
-
Sample Standard Deviation
n
-
Sample Size
i
For
unequal sample sizes
Differences in the Means
-
Tests for More than Two Populations
.
Differences in the Dispersion
Comparison
Test To
Use
Formula
Population Variance to a
Standard
c
2
-
Test
c
s
s
2
2
0
2
0
1
=
-
(
)
:
n
s
where
s
-
Sample Standard Deviation
-
"
Standard"
or Population Standard Deviation
n
-
Sample Size
Two Population
Variances
F
-
Test
Sample Standard Deviation
-
:
2
2
i
B
A
s
where
s
s
F
=
Differences in Proportions
Comparison
Test To
Use
Formula
Population Proportion to a
Standard
Z
-
Test
Z
p
n
where
p
=
-
-
P
P
P
0
0
0
1
(
)
/
:
-
Sample Proportion
n
-
Sample Size
Two Population
Proportions
Z
-
Test
(2 Pops)
Z
p
p
p
p
n
n
where
p
x
n
n
x
i
i
=
-
-
+
+
+
1
2
1
2
2
1
2
1
1
1
(
)
:
-
Sample Proportion
n
-
Sample Size
p
=
x
-
Number of Sample Items with Characteristic of Interest
i
1