hypothesis test formulas
DESCRIPTION
Hypothesis Test Formula for Six Sigma Project.TRANSCRIPT
-
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