The article \"Analysis of Time Headways on Urban Roads: CaseStudy from Riyadh\"

Question

The article "Analysis of Time Headways on Urban Roads: CaseStudy from Riyadh" (A. Al-Ghamdi, Journal of TransportationEngineering, 2001:289-294) presents a model for the time elapsedbetween the arrival of consecutive vehicles on urbal roads.Following are 137 arrival times (in seconds) along with the valuesexpected from a theoretical model. Time   Observed   Expected 0-2      28               23 2-4      28               18 4-6      14               16 6-8      7                 13 8-10    11               11 10-12   11               9 12-18   10              20 18-22   8                  8 >22      30               19 Can you conclude that the theoretical model does not explainthe observed values well? The article "Analysis of Time Headways on Urban Roads: CaseStudy from Riyadh" (A. Al-Ghamdi, Journal of TransportationEngineering, 2001:289-294) presents a model for the time elapsedbetween the arrival of consecutive vehicles on urbal roads.Following are 137 arrival times (in seconds) along with the valuesexpected from a theoretical model. Time   Observed   Expected 0-2      28               23 2-4      28               18 4-6      14               16 6-8      7                 13 8-10    11               11 10-12   11               9 12-18   10              20 18-22   8                  8 >22      30               19 Can you conclude that the theoretical model does not explainthe observed values well?

Explanation / Answer

Null Hypothesis: There is no evidence that thetheoretical model does not explain the observed valueswell Alternative Hypothesis: There is an evidencethat the theoretical model does not explain the observed valueswell Consider the following table Time Observed Expected (Oi-Ei)^2 (Oi-Ei)^2/Ei 0-2 28 23 25 1.086957 4-Feb 28 18 100 5.555556 6-Apr 14 16 4 0.25 8-Jun 7 13 36 2.769231 10-Aug 11 11 0 0 12-Oct 11 9 4 0.444444 18-Dec 10 20 100 5 18-22 8 8 0 0 >22 30 19 121 6.368421 chi-square 21.47461 Time Observed Expected (Oi-Ei)^2 (Oi-Ei)^2/Ei 0-2 28 23 25 1.086957 4-Feb 28 18 100 5.555556 6-Apr 14 16 4 0.25 8-Jun 7 13 36 2.769231 10-Aug 11 11 0 0 12-Oct 11 9 4 0.444444 18-Dec 10 20 100 5 18-22 8 8 0 0 >22 30 19 121 6.368421 chi-square 21.47461
The critical value of chi-square at (9-1)=8df and at0.05, the level of singificance is 15.51 Since the calcualted value of chik-squaer isgreater than the critical value of chi-square so we reject the nullhypothesis and conclude that there is an evidence that thetheoretical model does not explain the observed valueswell Time Observed Expected (Oi-Ei)^2 (Oi-Ei)^2/Ei 0-2 28 23 25 1.086957 4-Feb 28 18 100 5.555556 6-Apr 14 16 4 0.25 8-Jun 7 13 36 2.769231 10-Aug 11 11 0 0 12-Oct 11 9 4 0.444444 18-Dec 10 20 100 5 18-22 8 8 0 0 >22 30 19 121 6.368421 chi-square 21.47461

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