Final answer:
To evaluate whether the distribution of top safety picks has changed, one would perform a chi-square test. Total damage from accidents can be calculated by summing the costs of individual incidents. Assessing driver error as a cause for accidents involves statistical hypothesis testing for proportions.
Step-by-step explanation:
According to the Insurance Institute for Highway Safety, the risk of collision increases by various factors, but the exact percentage is not provided in the information you've given. However, analyzing data regarding car safety and accident rates can help determine risk factors and improve safety standards. For analyzing the distribution of cars that earned the top safety picks award between 2009 and 2013, one would use statistical methods to test for any significant changes. This can be performed by applying a chi-square test for independence at the given 5 percent significance level. Similarly, calculating the total damage incurred by a group of drivers, we consider the individual costs of different types of accidents and sum them for the group. In the simplified insurance example provided, the total calculation is based on the each group's individual accident costs.
Driver error is cited as a cause for a significant portion of fatal auto accidents. To test if a sample proportion (such as the 14 out of 30 fatal accidents caused by driver error) is consistent with the population proportion (54 percent according to the AAA), a hypothesis test for a proportion using alpha = 0.05 can be conducted.
For questions involving traffic collision mechanics, principles of physics such as conservation of momentum are used to determine the velocity of the wreckage after a collision. The calculation includes considering the masses of the vehicles and their respective velocities before the accident.