CE 436 Traffic Engineering

Topic 4: Statistics for Traffic Engineers

(Chapter 7)

Prof. Saad AlGadhi

CE 436 –Traffic Engineering

King Saud University

email: salgadhi@ksu.edu.sa

CE 436_KSU_Prof.AlGadhi2

CE 436_KSU_Prof.AlGadhi3

CE 436_KSU_Prof.AlGadhi4

CE 436_KSU_Prof.AlGadhi5

CE 436_KSU_Prof.AlGadhi6

CE 436_KSU_Prof.AlGadhi7

CE 436_KSU_Prof.AlGadhi8

CE 436_KSU_Prof.AlGadhi9

CE 436_KSU_Prof.AlGadhi10

CE 436_KSU_Prof.AlGadhi11

CE 436_KSU_Prof.AlGadhi12

CE 436_KSU_Prof.AlGadhi13

CE 436_KSU_Prof.AlGadhi14

CE 436_KSU_Prof.AlGadhi15

CE 436_KSU_Prof.AlGadhi16

CE 436_KSU_Prof.AlGadhi17

Figure 7.1 The Normal Distribution

CE 436_KSU_Prof.AlGadhi19

x N [ , 2 ]

CE 436_KSU_Prof.AlGadhi20

CE 436_KSU_Prof.AlGadhi21

z N [ 0, 1]

Figure 7.2 Shifting the Normal Distribution to the Standard Normal Distribution (Spot Speed)

x N [ 55, 49 ]

= 55 mph

= 7 mph

Examples p. 127

CE 436_KSU_Prof.AlGadhi 23

Table 7.3 The Standard Normal Distribution

Table 7.3 (continued) The Standard Normal Distribution

CE 436_KSU_Prof.AlGadhi26

Figure 7.1 The Normal Distribution

p ( ± 1.00) = 68.27 %

p ( ± 1.96) = 95.0 %

p ( ± 2.00) = 95.45 %

p ( ± 3.00) = 99.73 %

CE 436_KSU_Prof.AlGadhi28

CE 436_KSU_Prof.AlGadhi29

CE 436_KSU_Prof.AlGadhi30

CE 436_KSU_Prof.AlGadhi31

CE 436_KSU_Prof.AlGadhi32

CE 436_KSU_Prof.AlGadhi33

Confidence Intervals (Bounds)

CE 436_KSU_Prof.AlGadhi34

CE 436_KSU_Prof.AlGadhi35

CE 436_KSU_Prof.AlGadhi36

CE 436_KSU_Prof.AlGadhi37

CE 436_KSU_Prof.AlGadhi38

CE 436_KSU_Prof.AlGadhi39

CE 436_KSU_Prof.AlGadhi40

CE 436_KSU_Prof.AlGadhi41

CE 436_KSU_Prof.AlGadhi42

CE 436_KSU_Prof.AlGadhi43

CE 436_KSU_Prof.AlGadhi44

CE 436_KSU_Prof.AlGadhi45

CE 436_KSU_Prof.AlGadhi46

CE 436_KSU_Prof.AlGadhi47

CE 436_KSU_Prof.AlGadhi48

CE 436_KSU_Prof.AlGadhi49

CE 436_KSU_Prof.AlGadhi50

CE 436_KSU_Prof.AlGadhi51

CE 436_KSU_Prof.AlGadhi52

CE 436_KSU_Prof.AlGadhi53

CE 436_KSU_Prof.AlGadhi54

CE 436_KSU_Prof.AlGadhi55

CE 436_KSU_Prof.AlGadhi56

CE 436_KSU_Prof.AlGadhi57

CE 436_KSU_Prof.AlGadhi58

CE 436_KSU_Prof.AlGadhi59

CE 436_KSU_Prof.AlGadhi60

CE 436_KSU_Prof.AlGadhi61

CE 436_KSU_Prof.AlGadhi62

Example

Consider the spot speed data of Table 10.3 (p. 210) The computed mean was 48.1 mph and the computed standard deviation was 4.95 mph.

Consider the following hypothesis:

Ho, the underlying distribution is normal with =48.1 mph and =4.95 mph. See Table 10.3 (page 210)

N=12 categories, f=N-1-g=12-1-2=9 (# of degrees of freedom), =0.05, 2=16.92 (from Table 7.11, p.145)

Computed 2=14.3574<16.92 == > cannot reject Ho

CE 436_KSU_Prof.AlGadhi 63

Required Reading

Ch. 7: Statistical Applications in Traffic Engineering

All sections

CE 436_KSU_Prof.AlGadhi 64

HW # 3

Problems #:

7-1

7-2

7-3 (a & b only)

Due: Next Wednesday

CE 436_KSU_Prof.AlGadhi 65