Final answer:
To determine if the AAA proportion of fatal auto accidents caused by driver error is accurate, we perform a hypothesis test for proportion using the sample data of 30 fatal accidents, of which 14 involved driver error.
Step-by-step explanation:
The question asks us to determine if the American Automobile Association (AAA) statistic that 54 percent of all fatal auto accidents are caused by driver error holds true. This is a hypothesis testing problem involving proportions. We are given a sample of 30 fatal accidents, out of which 14 were caused by driver error. To determine if this sample data supports the AAA's claim, we would perform a hypothesis test for proportion.
First, we identify the null hypothesis (H0) as the proportion of fatal accidents caused by driver error being 0.54. The alternative hypothesis (H1) would be that the proportion is not equal to 0.54. We calculate the test statistic using the sample proportion and standard deviation, then compare this value to the critical value from a z-distribution at the significance level α = 0.05.
Upon performing these calculations, if the test statistic falls outside the acceptance region, we reject the null hypothesis, indicating that there is enough evidence to say that the AAA's proportion is inaccurate.