Math 2311
Class Notes for Section 8.3
8.3 – Comparing Two Means
Two – sample
t
– tests
compare the responses to two treatments or characteristics of two populations.
There is a separate sample from each treatment or population.
These tests are quite different than the
matched pairs
t
– test discussed in section 8.1.
How can we tell the difference between dependent and independent populations/samples?
The null and alternate hypotheses would be:
H
0
:
μ
1
=
μ
2
H
a
:
μ
1
>
μ
2
or
H
0
:
μ
1
=
μ
2
H
a
:
μ
1
<
μ
2
or
H
0
:
μ
1
=
μ
2
H
a
:
μ
1
≠
μ
2
And the assumptions for a twosample
t
– test are:
1.
We have two independent SRSs, from two distinct populations and we measure the same
variable for both samples.
2.
Both populations are normally distributed with unknown means and standard deviations.
(Or if
each given sample size is greater than or equal to 30.)
Twosample
t –
test
statistic:
t
=
(
x
1
−
x
2
)
−
(
μ
1
−
μ
2
)
s
1
2
n
1
+
s
2
2
n
2
The degrees of freedom is equal to the smaller of
n
1
−
1
and
n
2
−
1
.
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 Spring '08
 HAFEEZ
 Normal Distribution, Standard Deviation, 2%, allmale school

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