1
Homework 8 (20.4 pts + 1 pt Bonus)
due Nov. 4
(2 pts.) 8.46 (p.382). Three different design configurations are being considered for a
particular component. There are four possible failure modes for the component. An
engineer obtained the following data on number of failures in each mode for each of the
three configurations. Does the configuration appear to have an effect on type of failure?
Failure Mode
1
2
3
4
Total
Configuration 1
20
44
17
9
90
2
4
17
7
12
40
3
10
31
14
5
60
Total
34
92
38
26
190
1. The populations are the configurations, the categories are the failure modes and we are using
the population proportions, π
2. H
0
: the 3 different configurations are homogeneous with respect to failure mode
H
a
: H
0
is not correct
3. α = 0.05
4. See the contingency table for values.
?
=
??±
???²?³ ????´?
???²?³
?
µ¶²´??µ
?²????²?°???
=
90
³
(34)
190
= 16.105
which means that this value would go into the cell
(1,1)
The table with all of the values of both O and E are below with the E values in parentheses.
Failure Mode
1
2
3
4
Total
Configuration
1
20
(16.11)
44
(43.58)
17
(18.00)
9
(12.32)
90
2
4
(7.16)
17
(19.37)
7
(8.00)
12
(5.47)
40
3
10
(10.74)
31
(29.05)
14
(12.00)
5
(8.21)
60
Total
34
92
38
26
190
·
?
2
=
¸
(
¹ − ?
)
2
?
=
(20
−
16.11)
2
16.11
+
⋯
= 13.25
5.df = (4 – 1)(3 – 1) = 6
P(
·
6
2
<13.19) = 0.040, P(
·
6
2
<13.55) = 0.035
0.035 < P – value < 0.040
6. reject H
0
because 0.040 ≤ 0.05
7. The data does give strong support 0.035 < P – value < 0.040) to the claim that the probability
of the configurations depends on the type of failure mode.
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(2 pts.) #13. Are the following situations i) statistically significant, ii) practically
significant, iii) important? Please provide a brief explanation for each response. Note:
For each of the following situations, a minimum worthwhile change is 2.0 units.
a) The observed 90% CI is (1.8, 14) with a mean of 6.0 units and P = 0.20.
i) no because 0.20 > 0.1
ii) yes because 2.0 and greater is in the CI
iii) yes or maybe, since the value is practically significant, more statistical studies are needed to
see if the value is still in the CI when the study is statistically significant.
b) The observed 90% CI is (0.4, 3.4) with a mean of 2.0 units and P = 0.04.
i) yes because 0.04 ≤ 0.10
ii) yes because 2.0 and greater is in the CI
iii) yes since the study is both practically and statistically significant
c) The observed 90% CI is (0.4, 1.8) with a mean of 1.1 units and P = 0.007.
i) yes because 0.007 ≤ 0.10
ii) no because 2.0 is greater than the greatest value of the CI
iii) no, because there is no practical significance to the result
d) The observed 90% CI is (1.7, 2.3) with a mean of 0.3 units and P = 0.80.
i) no because 0.80 > any reasonable value of
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 Spring '08
 Staff
 Statistics, PROC GLM, mean bending parameter, Error Mean Square

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