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Anna Lee & Jery Stedinger
Fall 2006
CEE 304 – Section 9 Handout
(Two Sample Hypothesis Tests)
1.
Are men taller than women
as is often believed?
Look at the following data on heights (with units of inches) that was collected by former
CEE 304 students.
N
Mean
Median
Stdev
Women
4
65.146
64.500
2.441
Men
12
71.258
71.000
2.889
Let us consider these students to be a random sample of Cornell engineering students. Use
a ttest appropriate for small n.
Women’s height
Men’s height
__
__
y
= 71.258
x
= 65.146
s
x
= 2.441
s
y
= 2.889
n
x
= 4
n
y
= 12
σ
x
,
σ
y
UNKNOWN, small samples
Æ
Use ttest,
__
__
2
2
()
(
)
x
y
y
x
xy
XY
T
s
s
nn
μ
−−
−
=
+
(i)
What are the appropriate hypotheses?
Null Hypothesis
H
o
:
μ
x
=
μ
y
Alternative Hypothesis:
H
a
:
μ
x
<
μ
y
Æ
lowertailed test
(ii)
At the 1% level, what would be the rejection region for the test?
α = 1 %
Degrees of freedom:
2
2
2
42
11
y
x
yy
xx
s
s
sn
ν
⎛⎞
+
⎜⎟
⎝⎠
=
+
−
−
= 6
6
,
01
.
0
,
t
t
−
=
−
να
= 3.143
So, H
o
is rejected if
,
t
t
test
−
<
= 3.143 (lower tailed
t
test).
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 Fall '08
 Stedinger

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