Final answer:
To evaluate the American Automobile Association's proportion of 54 percent for driver error causing fatal accidents, a hypothesis test is used. The test statistic (z-value) is calculated from the sample, and if the resulting p-value is less than the significance level of 0.05, the null hypothesis is rejected, suggesting the AAA's proportion may not be accurate.
Step-by-step explanation:
To determine if the American Automobile Association's (AAA) proportion of 54 percent for driver error as the cause of fatal auto accidents is accurate, we can use a hypothesis test for a proportion. In the given scenario, 30 randomly selected fatal accidents are examined, and 14 were caused by driver error. We set the null hypothesis to be that the proportion of driver error is equal to 54 percent, which means the alternate hypothesis is that the proportion of driver error is not equal to 54 percent.
The test statistic for a single proportion is calculated using the following formula:
z = (p - P) / sqrt(P(1-P)/n)
Where:
- p is the sample proportion of accidents due to driver error (14/30).
- P is the hypothesized proportion of accidents due to driver error (0.54).
- n is the sample size (30).
Using the information given and the formula above, we can calculate the z-value, and then use a standard normal distribution table or software to find the p-value. If the p-value is less than the significance level alpha (α) of 0.05, we reject the null hypothesis, which would indicate that the AAA's proportion might not be accurate.