A model for the time elapsed between the arrival of consecutivevehicles on urban

Question

A model for the time elapsed between the arrival of consecutivevehicles on urban roads.
Following are 137 arrival times(in seconds) along with the valuesexpected from a theoretical model.

TIME   OBSERVED   EXPECTED
0-2             18                 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 explain theobserved value well?

Explanation / Answer

Null Hypothesis: the theoretical model does notexplain the observed value well Alternative Hypothesis: the theoretical modeldoes explain the observed value well Consider the following table TIME OBSERVED(Oi) EXPECTED(Ei) (Oi-Ei)^2 (Oi-Ei)^2/Ei 0-2 18 23 25 1.086957 2 to 4 28 18 100 5.555556 4 to 6 14 16 4 0.25 6 to 8 7 13 36 2.769231 8 to 10 11 11 0 0 10 to 12 11 9 4 0.444444 12 to 18 10 20 100 5 18-22 8 8 0 0 >22 30 19 121 6.368421 21.47461 TIME OBSERVED(Oi) EXPECTED(Ei) (Oi-Ei)^2 (Oi-Ei)^2/Ei 0-2 18 23 25 1.086957 2 to 4 28 18 100 5.555556 4 to 6 14 16 4 0.25 6 to 8 7 13 36 2.769231 8 to 10 11 11 0 0 10 to 12 11 9 4 0.444444 12 to 18 10 20 100 5 18-22 8 8 0 0 >22 30 19 121 6.368421 21.47461
The critical value of chi-square at (9-1) =8df andat 0.05, the level of significance is 15.51 Since the p-value is greater than the criticalvalue of chi-square so we reject the null hypothesis and concludethat the theoretical model does explain the observed valuewell
TIME OBSERVED(Oi) EXPECTED(Ei) (Oi-Ei)^2 (Oi-Ei)^2/Ei 0-2 18 23 25 1.086957 2 to 4 28 18 100 5.555556 4 to 6 14 16 4 0.25 6 to 8 7 13 36 2.769231 8 to 10 11 11 0 0 10 to 12 11 9 4 0.444444 12 to 18 10 20 100 5 18-22 8 8 0 0 >22 30 19 121 6.368421 21.47461

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