Question

What Percentage of Auto Accidents are Caused by Human Error?

Answer 1

The AAA states that 54% of fatal auto accidents are due to driver error, and a study with 30 cases found 14 due to such errors. Statistical analysis can be used to confirm the accuracy of this proportion considering a significance level of 0.05.

Step-by-step explanation:

The question focusses on whether the proportion of auto accidents caused by human error provided by the American Automobile Association (AAA) is accurate. According to AAA, approximately 54 percent of all fatal auto accidents are due to driver error. A study of 30 randomly selected fatal accidents found that 14 were caused by driver error. To determine if the AAA percentage is accurate, statistical methods such as hypothesis testing can be applied using the significance level (α = 0.05). For instance, a safety engineer who predicts that 35 percent of industrial accidents are due to not following instructions might use similar statistical analysis to validate her hypothesis.

Answer 2

Using statistical hypothesis testing and a significance level of 0.05, the provided data on fatal auto accidents can be analyzed to confirm or refute the American Automobile Association's claim that 54 percent of such accidents are caused by driver error.

Step-by-step explanation:

The question involves using statistics to determine whether the American Automobile Association's statement that 54 percent of all fatal auto accidents are caused by driver error is accurate.

A sample of 30 randomly selected fatal accidents is reviewed, with 14 found to be caused by driver error. A hypothesis test can be applied here, using an alpha level (a) of 0.05 to decide if the observed proportion of 14 out of 30, which is approximately 46.67 percent, significantly differs from the AAA's reported 54 percent.

The evaluation process would involve calculating the test statistic and comparing it to a critical value, or using a p-value approach to determine if there is enough evidence to reject the AAA's claimed proportion.

If the test statistic is beyond the critical value or the p-value is less than 0.05, we would reject the AAA's claim in favor of the alternative hypothesis that the proportion of accidents caused by driver error is different than 54 percent. This problem is a practical application of hypothesis testing in statistics to assess proportions.