Download HW #5 – Categorical Analysis CIVL 7012 Due Wednesday, April 1

HW #5 – Categorical Analysis
CIVL 7012
Due Wednesday, April 1, 2009
1. 9-91
2. The ultimate strains of 15 #5 steel reinforcing bars were measured, yielding
the results shown below.
a. Perform a chi-square test for the normal distribution at a significance
level of 0.05.
b. Perform the Kolmogorov-Smirnov test for the normal distribution at a
significance level of 0.05.
c. Based on the data and the results of the tests, which do you think is
most appropriate for this data?
Bar #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Ultimate Strain, U (%)
19.4
16.0
16.6
17.3
18.4
17.9
17.8
18.8
20.1
19.1
16.1
16.8
17.0
18.1
18.6
3. The exponential distribution is often used to model the time to failure of
mechnical equiment. In order to verify the distribution of a certain type of
diesel engine, a large number of units of the engine were tested, and the time
to failure of each, in hours, was recorded as tabulated below.
a. Perform the chi-square test to evaluate the validity of the exponential
distribution at the 5% significance level.
b. Perform a Kolmogorov-Smirnov test for the exponential distribution
at the same signficance level.
c. Discuss any differences in the results between the two tests.
Time to failure (hr) of Diesel Engines
0.13
0.78
3.55
14.29
54.85
216.40
1296.93
952.65
8.82
29.75
121.58
672.87
62.09
656.04
735.89
895.80
1057.57
470.97
151.44
163.95
2959.47
124.09
85.28
380.00
298.58
678.13
861.93
1885.22
862.93
1407.52
2.34
393.37
84.09
646.01
412.03
813.00
39.10
633.98
658.38
855.95