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(IELM313)Hw2.pdf
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IELM313 Homework 2
Due 20 March 2006, before class starts
1. The highway between Shanghai and Hang Zhou has a high incidence of accidents along its 100 kilometers. Police officers say that the occurrence of accidents along the highway is randomly (uniformly) disturbed, but the news media say otherwise. The Shanghai government published records for the month of January. These records indicated the point at which 30 accidents involving an injury or death occurred, as follows (the data points representing the distance from the city limits of Shanghai):
88.3 40.7 36.3 27.3 36.8
91.7 67.3 7.0 45.2 23.3
98.8 90.1 17.2 23.7 97.4
32.4 87.8 69.8 62.6 99.7
20.6 73.1 21.6 6.0 45.3
76.6 73.2 27.3 87.6 87.2
Use the Kolmogorov-Smirnov test to discover whether the distribution of location of accidents is uniformly distributed for the month of January.
2. The time required for 50 different employees to compute and record the number of hours worked during the week was measured, with the following results in minutes:
No. Time No. Time No. Time No. Time
1 1.88 14 0.79 27 1.49 40 4.29
2 0.54 15 0.21 28 0.66 41 0.80
3 1.90 16 0.80 29 2.03 42 5.50
4 0.15 17 0.26 30 1.00 43 4.91
5 0.02 18 0.63 31 0.39 44 0.35
6 2.81 19 0.36 32 0.34 45 0.36
7 1.50 20 2.03 33 0.01 46 0.90
8 0.53 21 1.42 34 0.10 47 1.03
9 2.62 22 1.28 35 1.10 48 1.73
10 2.67 23 0.82 36 0.24 49 0.38
11 3.53 24 2.16 37 0.26 50 0.48
12 0.53 25 0.05 38 0.45
13 1.80 26 0.04 39 0.17

a.
Create a histogram.

b.
One can easily find the average working hours are 1.206 minutes. Use the chi-square test to test the hypothesis that these service times are exponentially distributed with mean 1.206 minutes. Use the level of significance =0.05.

c.
Create a q-q plot assuming the data are exponentially distributed with mean 1.206 minutes. Do you think the distribution fits the data well?