Chapter Ten
10.1
The two samples are independent if they are drawn from two different populations and the elements of
the two samples are not related. As an example, suppose we want to estimate the difference between
the salaries of male and female university professors. To do so, we will select two samples from two
different populations, one from all male university professors and the second from all female
university professors. These two populations will include different elements that are not related.
In two dependent samples, the elements of one sample are related to the elements of the second
sample. To test if a certain course that claims to reduce stress, does indeed decrease stress, we will
take a sample of people who are suffering from stress. We will measure the stress level for these
people before they take this course and then after they finish it. Based on these results we will make a
decision. Notice, that in this example, we have the same group of people for two samples of data, one
before taking the course and the second after completing the course.
10.3
a.
The point estimate of
μ
1
–
μ
2
is
2
1
x
x

= 5.56 – 4.80 = .76
2
1
x
x
s

=
=
+
2
2
2
1
2
1
n
s
n
s
=
+
270
)
58
.
1
(
240
)
65
.
1
(
2
2
.14349103
Margin of error =
28
.
)
14349103
(.
96
.
1
96
.
1
2
1
±
=
±
=
±

x
x
s
b.
The
z
value for the 99% confidence level is 2.58.
The 99% confidence interval for
μ
1
–
μ
2
is:
2
1
)
(
2
1
x
x
zs
x
x

±

= .76
±
2.58 (.14349103) = 0.76
±
.37 = .39 to 1.13
TI83
: Select STAT, TESTS, 9: 2SampZInt, and press the ENTER key. If you have summary
statistics highlight Stats otherwise select Data. Here we have summary statistics and will choose Stats
and press the ENTER key. We then use the down arrow to scroll down to enter the requested
information for the first sample followed by the information from the second sample. In this example
its
1
x
= 5.56, σ1=
s
1
= 1.65,
n
1
= 240,
2
x
= 4.80, σ2=
s
2
= 1.58,
n
2
= 270, CLevel: = .99 for the
Confidence level, highlight No for pooled data, highlight Calculate, and press the ENTER key.
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Chapter Ten
2
−
SampZInt
(.39039, 1.1296)
=
1
x
5.56
=
2
x
4.8
n
1
= 240
n
2
= 270
10.5
H
0
:
μ
1
–
μ
2
= 0;
H
1
:
μ
1
–
μ
2
≠ 0
For
α
= .05, the critical values of
z
are –1.96 and 1.96.
From Exercise 10.3,
2
1
x
x
s

= .14349103
=



=

2
1
)
(
)
(
2
1
2
1
x
x
s
x
x
z
μ
μ
30
.
5
14349103
.
0
)
80
.
4
56
.
5
(
=


Reject
H
0
.
TI83
: Select STAT, TESTS, 3: 2SampZTest, and press the ENTER key. If you have summary
statistics highlight Stats otherwise select Data. Here we have summary statistics and will choose Stats
and press the ENTER key. We then use the down arrow to scroll down to enter the requested
information for the first sample followed by the information from the second sample. In this example
its σ1=
s
1
= 1.65, σ2=
s
2
= 1.58,
1
x
= 5.56,
n
1
= 240,
2
x
= 4.80,
n
2
= 270, for
μ
1
highlight ≠
μ
2
as this is a
two tailed test, highlight Calculate, and press the ENTER key. The results are shown below and from
them we can see that in this example we reject the null hypothesis.
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 Fall '07
 Guggenberger
 Statistics, Normal Distribution, Statistical hypothesis testing, Enter key

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