STAT 420
Examples #17
Spring 2008
1.
We wish to test whether coffee stunts the growth of children. We obtain a
random sample of 6 adult males who started drinking coffee regularly before
the age of 14, and a random sample of 8 adult males who did not drink coffee
regularly before the age of 14. The heights of the 14 individuals in inches are
as follows:
Coffee:
65, 68, 67, 66, 71, 68.
No Coffee:
68, 70, 67, 71, 70, 72, 73, 69.
Assume that the populations are approximately normally distributed, and that
the overall variances are equal.
a)
Compute
1
y
,
2
y
,
2
1
s
, and
2
2
s
.
n
= 6
m
= 8
6
405
=
=
n
x
x
= 67.5
8
560
=
=
m
y
y
= 70
x
x
x

( )
2
x
x

y
y
y

( )
2
y
y

65
–
2.5
6.25
68
–
2
4
68
0.5
0.25
70
0
0
67
–
0.5
0.25
67
–
3
9
66
–
1.5
2.25
71
1
1
71
3.5
12.25
70
0
0
68
0.5
0.25
72
2
4
0
21.5
73
3
9
69
–
1
1
0
28
( )
5
5
.
21
1
2
2
1
=
=


n
x
x
s
= 4.3
( )
7
28
1
2
2
2
=
=


m
y
y
s
= 4
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Test for difference in the average heights for these two groups using the
t
test
and pooled variance. Use a 5% level of significance. What can you say about
the pvalue of this test?
( ) ( )
2
1
1
2
1
2
2
2
2
1
1
2
pooled

+

+

=
⋅
⋅
n
n
s
n
s
n
s
To test
H
0
:
μ
1
–
μ
2
=
δ
0
Assumptions:
1) Both populations are
normal.
2) The population standard
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 Spring '08
 STEPANOV
 Statistics, Normal Distribution, Statistical hypothesis testing, oats, MSW, average thiamin content

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