Final answer:
The driver error makes up 26% of all collisions. A hypothesis test is conducted to determine if the AAA proportion is accurate. The null hypothesis is not rejected, indicating that there is not enough evidence to conclude that the AAA proportion is inaccurate.
Step-by-step explanation:
The answer is 26 percent. According to the given information, 54 percent of all fatal auto accidents are caused by driver error. In a sample of 30 fatal accidents, 14 were caused by driver error. To determine if the AAA proportion is accurate, we can conduct a hypothesis test at a significance level of 0.05.
We will use the proportion test for hypothesis testing. The null hypothesis, denoted as H0, is that the AAA proportion is accurate at 54 percent. The alternative hypothesis, denoted as HA, is that the AAA proportion is not accurate. We will use a two-tailed test.
We calculate the test statistic using the formula: Z = (p - P0) / √((P0(1 - P0)) / n), where p is the sample proportion, P0 is the population proportion, and n is the sample size. Substituting the given values into the formula, we get: Z = (14/30 - 0.54) / √((0.54 * 0.46) / 30) ≈ -0.6365.
We then compare the test statistic to the critical values associated with a significance level of 0.05. If the test statistic falls within the critical region, we reject the null hypothesis. If it falls outside the critical region, we fail to reject the null hypothesis. In this case, the absolute value of the test statistic is less than the critical value of 1.96, so we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the AAA proportion is inaccurate.