Chapter 7: Statistics Application
147
0703
To
specify
> 120,
σ
= 19 for the data in lists to the right (list1 = data, list2 =
frequency) and perform a 1-Sample
Z
Test
2-Sample
Z
Test
.... [Test] - [Two-Sample Z-Test] .....
Tests the difference between two means when the standard deviations of the two populations are known. The
normal distribution is used for the 2-Sample
Z
test.
1-Proportion
Z
Test
.... [Test] - [One-Prop Z-Test] .....
z
= (
x
/
n
–
p
0
)/
p
0
(1 –
p
0
)/
n
Tests a single sample proportion against the known proportion of the null hypothesis. The normal distribution is
used for the 1-Proportion
Z
test.
2-Proportion
Z
Test
.... [Test] - [Two-Prop Z-Test] .....
z
= (
x
1
/
n
1
–
x
2
/
n
2
)/
pˆ
(1 –
pˆ
)(1/
n
1
+ 1/
n
2
)
Tests the difference between two sample proportions. The normal distribution is used for the 2-Proportion
Z
test.
1-Sample
t
Test
.... [Test] - [One-Sample
t
-Test] .....
t
= (
o
–
μ
0
)/(s
x
/
'
n
)
Tests a single sample mean against the known mean of the null hypothesis when the population standard
deviation is unknown. The
t
distribution is used for the 1-Sample
t
test.
2-Sample
t
Test
.... [Test] - [Two-Sample
t
-Test]
Tests the difference between two means when the standard deviations of the two populations are unknown.
The
t
distribution is used for the 2-Sample
t
test.
When the two population standard deviations are
equal (pooled)
= (
o
1
−
o
2
)/ s
2
(1/
1
+ 1/
2
)
=
1
+
2
− 2
s
= ((
1
− 1)s
1
2
+ (
2
− 1)s
2
2
)/(
1
+
2
− 2)
When the two population standard deviations are not
equal (not pooled)
= (
o
1
−
o
2
)/ s
1
2
/
1
+ s
2
2
/
2
= 1/(
2
/(
1
− 1) + (1 −
)
2
/(
2
− 1))
= (s
1
2
/
1
)/(s
1
2
/
1
+ s
2
2
/
2
)
Linear Regression
t
Test
.... [Test] - [Linear Reg
t
-Test] .....
=
(
− 2)/(1 −
2
)
= (
−
o
)(
−
p
)/ (
−
o
)
2
=
p
−
o
Y
Y
n
: sample size (
n
t
3)
Tests the linear relationship between the paired variables (
x
,
y
). The method of least squares is used to
determine
a
and
b
, which are the coefficients of the regression formula
y
=
a
+
bx
. The
p
-value is the probability
of the sample regression slope (
b
) provided that the null hypothesis is true,
"
= 0. The
t
distribution is used for
the linear regression
t
test.
