Final answer:
To test the AAA's claim that driver error causes 54% of fatal auto accidents, we set up null and alternative hypotheses and use a statistical hypothesis test with a significance level of 0.05 to compare the observed proportion of driver error accidents against the claimed proportion.
Step-by-step explanation:
The question pertains to hypothesis testing in statistics to determine if the American Automobile Association's assertion that driver error is the cause of approximately 54% of all fatal auto accidents is accurate.
Given that 14 out of 30 randomly selected fatal accidents were caused by driver error, we can perform a hypothesis test with a significance level of α = 0.05.
Firstly, null and alternative hypotheses must be set up:
- H0 (Null Hypothesis): p = 0.54 - The proportion of accidents caused by driver error is 54%
- Ha (Alternative Hypothesis): p ≠ 0.54 - The proportion of accidents caused by driver error is not 54%
We then perform the appropriate statistical test (such as a one-proportion z-test) to determine if the observed proportion of 14 out of 30, which is approximately 46.67%, is significantly different from the claimed proportion of 54%.