Final answer:
The question is about determining if the sample data on driver error in fatal accidents significantly differs from the proportion reported by the AAA. A hypothesis test is used with an α of 0.05 to compare the sample proportion to the claimed proportion. The test would involve calculating a test statistic and comparing it to a critical value to accept or reject the null hypothesis.
Step-by-step explanation:
The question is addressing the concept of driver error as a contributing factor to vehicle crashes and whether the American Automobile Association's (AAA) reported proportion is accurate. When conducting a hypothesis test for a proportion, one must use the sample data to see if it significantly differs from the claimed proportion.
With 14 out of 30 fatal accidents being caused by driver error, we can set up a hypothesis test using the significance level (α) of 0.05 to determine if this sample proportion of approximately 46.67% (14/30) significantly differs from the AAA's claimed proportion of 54%.
To conduct this test, one would calculate the test statistic using the sample proportion, the claimed proportion, and the sample size, and then compare this test statistic to a critical value from the standard normal distribution corresponding to the chosen α level.
If the test statistic falls into the critical region, we reject the null hypothesis that the true proportion is equal to the claimed proportion. Otherwise, we do not reject the null hypothesis, implying that the sample data does not provide strong evidence against the AAA proportion.