Final answer:
The total damage incurred by car accidents for 100 drivers, with large accidents resulting in $150,000 and smaller ones adding up to $36,000, equates to $186,000. To cover these costs, each driver can pay a $1,860 premium annually. The accuracy of the AAA statement on driver error can be tested statistically with an appropriate significance level.
Step-by-step explanation:
When considering the total damage of car accidents among a group of 100 drivers, if we assume that 10 drivers have large accidents with damages costing $15,000 each, the calculation for the total damage would be as follows. Imagine the remaining 90 drivers have smaller accidents costing a total of $36,000. The accumulation of all these costs ($150,000 from large accidents + $36,000 from small accidents) results in a total damage figure of $186,000.
From an insurance perspective, to cover these costs, each of the 100 drivers would need to pay an annual premium of $1,860. If the insurance company sets the premiums at this amount, it can collect the necessary funds to cover the damages from accidents, presuming the occurrence of accidents is similar to past data.
Assessing the accuracy of the American Automobile Association's (AAA's) statement that driver error is the cause of 54 percent of all fatal auto accidents can be done using statistical hypothesis testing. An example scenario would be analyzing 30 randomly selected fatal accidents and finding 14 cases of driver error.
With a significance level of alpha = 0.05, a statistical test could determine if the observed proportion significantly deviates from the AAA's reported proportion.