Whether there was a statistically significant difference in the average speeds, the mean speed, standard deviation, 85th percentile speed and percentage of traffic exceeding the posted speed limit of 30 mi/h.
Answer to Problem 9P
Significant reduction
Explanation of Solution
Given:
Significance level of
Formula used:
S is standard deviation
N is number of observations
Spis square root of the pooled variance
S1 and S2 are standard deviations of the populations
T is the test static
Calculation:
Before an increase in speed enforcement activities:
The speed ranges from 28 to 40 mi/hgiving a speed range of 12. For five classes, the range per class is 2.4mi/h. A frequency distribution table can then be prepared, as shown below, in which the speed classes are listed in column 1 and the mid-values are in column 2. The number of observationsfor each class is listed in column 3, the cumulative percentages of all observations arelisted in column 6.
1 | 2 | 3 | 4 | 5 | 6 | 7 |
Speed class (mi/h) | Class mid-value | Class frequency, | | Percentage of class frequency | Cumulative percentage of class frequency | |
28-30 | 29 | 4 | 116 | 13 | 13 | 139.24 |
31-33 | 32 | 5 | 160 | 17 | 30 | 42.05 |
34-36 | 35 | 12 | 420 | 40 | 70 | 0.12 |
37-39 | 38 | 6 | 228 | 20 | 90 | 57.66 |
40-42 | 41 | 3 | 123 | 10 | 100 | 111.63 |
Total | 30 | 1047 | 350.7 |
Determine the arithmetic mean speed:
Determine the standard deviation:
The 85th-percentile speed is obtained from the cumulative frequency distribution curve as 36 mi/h.
The percentage of traffic exceeding the posted speed limit of 30 mi/h is 76 %.
Below given figure shows the cumulative frequency distribution curve for the data given. In this case, the cumulative percentages in column 6 of the above Table are plotted against the upper limit of each corresponding speed class. This curve, therefore, gives the percentage of vehicles that are traveling at or below a given speed.
After an increase in speed enforcement activities:
The speed ranges from 20 to 37 mi/h giving a speed range of 17. For six classes, the range per class is 2.83 mi/h. A frequency distribution table can then be prepared, as shown below in which the speed classes are listed in column 1 and the mid-values are in column 2. The number of observations for each class is listed in column 3, the cumulative percentages of all observations are listed in column 6.
1 | 2 | 3 | 4 | 5 | 6 | 7 |
Speed class (mi/h) | Class mid-value | Class frequency, | | Percentage of class frequency | Cumulative percentage of class frequency | |
20-22 | 21 | 6 | 126 | 20 | 20 | 253.5 |
23-25 | 24 | 8 | 192 | 27 | 47 | 98 |
26-28 | 27 | 4 | 108 | 13 | 60 | 1 |
29-31 | 30 | 3 | 90 | 10 | 70 | 18.75 |
32-34 | 33 | 5 | 165 | 17 | 87 | 151.25 |
35-37 | 36 | 4 | 144 | 13 | 100 | 289 |
Total | 30 | 825 | 811.5 |
Determine the arithmetic mean speed:
Determine the standard deviation:
Below given figure shows the cumulative frequency distribution curve for the data given. In this case, the cumulative percentages in column 6 of the above Table are plotted against the upper limit of each corresponding speed class. This curve, therefore, gives the percentage of vehicles that are traveling at or below a given speed.
The 85th-percentile speed is obtained from the cumulative frequency distribution curve as 31.5 mi/h.
The percentage of traffic exceeding the posted speed limit of 30 mi/h is 24 %.
Determine square root of the pooled variance:
Compute test static T:
Determine whether
From Appendix A, theoretical
Since
Conclusion:
The increase in speed enforcement activities has resulted in a significant reduction in the mean speed on the street at a significance level of 0.05. The mean speeds before and after increase in speed enforcement activities are 35.1 and 27.47 mi/h respectively. The standard deviations are 3.5 and 5.3 mi/h respectively. The 85th percentile speeds are 36 mi/h and 31.5 mi/h and percentages of traffic exceeding the posted speed limit of 30 mi/h are 76 % and 24 %.
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