SECTION 9.3
213
(b) The sample means are
X
1
1 998,
X
2
3 0000,
X
3
5 300. The sample sizes are
J
1
5,
J
2
J
3
3. The up
per 5% point of the Studentized range is
q
3 8 05
4 04. The 5% critical value for
X
1
X
2
and for
X
1
X
3
is
4 04
1 3718 2
1 5
1 3
2 44, and the 5% critical value for
X
2
X
3
is 4 04
1 3718 2
1 3
1 3
2 73. Therefore means 1 and 3 differ at the 5% level.
13. (a)
X
88 04,
I
4,
J
5,
MSTr
∑
I
i
1
J
X
i
X
2
I
1
19 554.
F
MSTr MSE
19 554 3 85
5 08.
There are 3 and 16 degrees of freedom, so 0 01
P
0 05
(a computer package gives
P
0 012). The null hypothesis of no difference is rejected at the 5% level.
(b)
q
4 16 05
4 05, so catalysts whose means differ by more than 4 05
3 85 5
3 55 are significantly different
at the 5% level. Catalyst 1 and Catalyst 2 both differ significantly from Catalyst 4.
15.
The value of the
F
statistic is
F
MSTr MSE
19 554 MSE. The upper 5% point of the
F
3 16
distribution is
3.24. Therefore the
F
test will reject at the 5% level if 19 554 MSE
3 24, or, equivalently, if MSE
6 035.
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 Fall '11
 MattGilg
 Statistics, Null hypothesis, Studentized range, piston ring type

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