Chapter 7: Statistics Application
141
Tests
The
Z
Test provides a variety of different tests based on standard deviation based tests. They make it possible
to test whether or not a sample accurately represents the population when the standard deviation of a
population (such as the entire population of a country) is known from previous tests. The
t
Test is used instead
of the
Z
Test when the population standard deviation is unknown. You can also perform
χ
2
Test, ANOVA
(analysis of variance), and other test calculations.
The following describes the ClassPad commands for executing each type of statistical test calculation. It
includes the calculation formula used and a general overview of each command.
1-Sample
Z
Test
.... [Test] - [One-Sample Z-Test] .....
z
= (
o
–
μ
0
)/(
σ
/
'
n
)
Tests a single sample mean against the known mean of the null hypothesis when the population standard
deviation is known. The normal distribution is used for the 1-Sample
Z
test.
0702
To
specify
≠
0,
σ
= 3 for
n
(sample size) = 48,
o
(sample mean) = 24.5 data and perform a 1-Sample
Z
Test
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
)
