Question

Traffic engineers are concerned about the rear end collisions that take place at intersections that have a stoplight. When drivers abruptly stop at a yellow light because they are concerned about making it through the intersection, the driver of the car behind theirs may not have anticipated them stopping and a collision occurs. For a 45 mph speed zone, typically the yellow light duration is set at 4.2 seconds. Traffic engineers wonder if setting that duration for a shorter or a longer time might help reduce rear end collisions. The traffic engineers randomly set a traffic light at a moderately busy intersection on the same day of each week, at the same time, and during good driving weather to have durations of 3.2 seconds, 4.2 seconds, and 5.2 seconds. They expect that there will be fewer rear end collisions when the yellow light is of a longer duration.

Using the 0.05 level of significance, analyze the following data and complete the following worksheet by filling in the blanks.

Yellow light duration time (in seconds)	Number of rear end collisions
3.2	12
3.2	12
3.2	11
3.2	10
4.2	9
4.2	10
4.2	11
4.2	11
5.2	9
5.2	8
5.2	8
5.2	7

Answer 1

Here, we conduct One-way ANOVA test to determine whether there is significant difference between average number of rear end collisions for difference yellow light duration time.

Hence, we there is sufficient evidence that there is significant difference between average number of rear end collisions for difference yellow light duration time.

Now, we conduct Post-hoc test to check which two groups are significantly different from each other .

Results are :

Treatments pair	Tukey HSD Q statistic	Tukey HSD   p-value	Tukey HSD inferfence
A vs B	2.1909	0.3149512	insignificant
A vs C	7.1204	0.0018152	** p<0.01
B vs C	4.9295	0.0169893	* p<0.05

Here,

A : Yellow light duration is set at 3.2 seconds

B : Yellow light duration is set at 4.2 seconds

C : Yellow light duration is set at 5.2 seconds

We can see that there is significant difference between average number of rear end collisions when Yellow light duration is set at 3.2 seconds and Yellow light duration is set at 5.2 seconds

Also, There is significant difference between average number of rear end collisions when Yellow light duration is set at 4.2 seconds and Yellow light duration is set at 5.2 seconds

Hence, overall we can say that there will be fewer rear end collisions when the yellow light is of a longer duration.