Final answer:
The question involves conducting a hypothesis test for proportions to determine if the sample data on driver error in fatal accidents is consistent with the American Automobile Association's reported proportion. By comparing the p-value obtained from the z-test with the significance level of 0.05, one can conclude whether there is a significant difference.
Step-by-step explanation:
To test if the American Automobile Association's (AAA) proportion of fatal accidents caused by driver error is accurate, we can use a hypothesis test for proportions. Given that AAA claims that driver error is the cause of about 54% of all fatal auto accidents, and we have a sample of 30 accidents where 14 were caused by driver error, we want to test if the sample proportion (14/30) significantly differs from the claimed proportion (0.54).
Our null hypothesis (H0) is that the true proportion of accidents caused by driver error is equal to the reported proportion by AAA, p0 = 0.54. Our alternative hypothesis (H1) is that the true proportion is not equal to 0.54. Using a significance level of α = 0.05, we can perform a z-test for the proportion and calculate the z-statistic and the p-value.
If the p-value is less than 0.05, we reject the null hypothesis, suggesting that the proportion of 14 out of 30 fatal accidents due to driver error is significantly different from AAA's reported proportion. Otherwise, we do not have enough evidence to claim that there is a difference.