user manual

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
)