Question $3(15$ pts$.)$: An engineer knows that one countermeasure has a crash reduction factor of $0\mathrm{.}1($i$.$e$.,C{R}_1=0\mathrm{.}1).$ If he were to implement it together with a second countermeasure, it would result in an overall crash reduction factor of $0\mathrm{.}15.$ If he were to implement these two countermeasures with a third one, it would result in an overall crash reduction factor of $0\mathrm{.}3.$ what must $C{R}_2$ and $C{R}_3$ be$?$ If all three countermeasures are implemented at $100$ locations throughout the city, determine if it can be concluded, based on the following projected data, that there is a significant decrease in crashes at the $93\%$ confidence level. Clearly state your hypothesis, test statistic, critical value, and rejection$/$acceptance criterion. The standard normal table is provided on the last page of the exam.

Do Nothing

Mean number of crashes per year $=5$

Standard deviation of crashes per year $=1\mathrm{.}5$

Sample size $=100$

All $3$ Countermeasures Implemented

Mean number of crashes per year $3$

Standard deviation of crashes per year $=0\mathrm{.}9$

Sample size $=100$