Islamic University of Gaza
Faculty of Engineering
Industrial Engineering Department
EIND4303: Design of experiment
Spring Semester 2010
Instructor: Mohammad Abuhaiba, Ph.D., P.E
TA: Said Matar and Duaa Abu-Dagga
Problem 2.11: The following are the burning times (in minutes) of chemical flares of two
different formulations. The design engineers are interested in both the means and variance of the
burning times.
Type 1
Type 2
65
81
57
66
82
82
67
59
75
70
64
71
83
59
65
56
69
74
82
79
(a) Test the hypotheses that the two variances are equal. Use α = 0.05
H0:
=
H1:
≠
Since the hypothesis test two variances, so the F-test will be used to prove the hypothesis
S1 = 9.264
=10
, Since
S2 = 9.367
=10
so we accept H0
(b)Test the hypotheses that the mean burning times are equal. Use α = 0.05.
Since the population of these two samples is unknown, so the t-test will be used to prove the
hypothesis
H0: μ1 = μ2
H1: μ1 ≠ μ2
Assuming that
=
=
=9.32
= 0.048
Since
so we accept H0
Claim was true that means of the burning times are equal
(b) Discuss the role of the normality assumption in this problem. Check the
assumption of normality for both types of flares.
R-square for the two types are .965 and .990 respectively, so normality assumption is valid.
The assumption of normality is required in the theoretical development of the t-test. However,
moderate departure from normality has little impact on the performance of the t-test. The
normality assumption is more important for the test on the equality of the two variances. An
indication of no normality would be of concern here. The normal probability plots shown below
indicate that burning time for both formulations follow the normal distribution.
Probability Plot of Type 1
Normal - 95% CI
99
95
90
80
Percent
70
60
50
40
30
20
10
5
1
30
40
50
60
70
80
90
100
110
Probability Plot of Type 2
Normal - 95% CI
99
95
90
80
Percent
70
60
50
40
30
20
10
5
1
30
40
50
60
70
80
90
100
110
Problem 2.17:
(a) Construct normal probability plots for both samples. Do these plots support
assumptions of normality and equal variance for both samples?
R-square for the Formulation 1and formulation 2 are .943 and .934 respectively, so normality
assumption is valid. The slopes for the two formulations are 2.868 and 2.919 and approximately
they are similar so the equal variance assumption is valid
Probability Plot of Formulation 1
Normal - 95% CI
99
95
90
80
Percent
70
60
50
40
30
20
10
5
1
160
170
180
190
200
210
220
230
Probability Plot of Formulation 2
Normal - 95% CI
99
95
90
80
Percent
70
60
50
40
30
20
10
5
1
150
160
170
180
190
200
210
220
230
(b) Do the data support the claim that the mean deflection temperature under load for
formulation 1 exceeds that of formulation 2? Use α = 0.05.
Since the population of these two samples is unknown, so the t-test will be used to prove the
hypothesis
H0: μ1 = μ2 (P.O.I)
H1: μ1 > μ2 (Claim)
S1 = 10.18
S2 = 9.949
=12
=12
υ=22
,
, since
so we accept H0
So mean deflection temperature under load for formulation 1 does not exceed formulation 2
(c) What is the P-value for the test in part (a)?
From t-table:
P  .4 .341  .256

, P=.37
.4  .25 .256  .686