Question $1$

$[20/100$ marks$]$

$(1)$ The radius of a horizontal curve on an existing road is $250m.$ The superelevation rate at the curve is $0\mathrm{.}08,$ and the posted speed limit on the road is $65k\frac{m}{h}.$ Is this a hazardous location? If so$,$ why? What action will you recommend to correct the situation? $[8/20]$

From the Manual for Roads and Bridge, Superelevation rate can be calculated using:

$S=\frac{V^2}{2\mathrm{.}828R}$

$(2)$ Collision data collected for three consecutive years at the curve show that $10$ collisions occurred during the $3-$year period. Data collected at $10$ other locations with similar geometric and traffic characteristics give the information shown in the table. Determine whether this type of crash is overrepresented at the study site for a $95\%$ confidence level $)=(1\mathrm{.}96.[12/20]$

Table Q$1$

$\backslash$table$[[$Control Site$],[1,$Number of Collisions$],[2,8],[3,5],[4,7],[5,8],[6,6],[7,8],[8,9],[9,10],[10,6]]$