Final answer:
The question involves a hypothesis test to determine if the average wait time is more than 6 minutes, with a significance level of 0.03. The appropriate test is a one-sample z-test given the known population standard deviation. The null hypothesis is set at a mean of 6 minutes and is tested against the alternative that the mean is greater.
Step-by-step explanation:
The subject of the question is Mathematics, specifically hypothesis testing in statistics. The scenario mentioned involves a state Department of Transportation claiming that the mean wait time is more than 6 minutes. The significance level α is set to 0.03. A one-sample z-test is appropriate here as the population standard deviation is known.
Hypothesis Test
The null hypothesis (H0) for this test would be μ = 6, and the alternative hypothesis (H1) would be μ > 6.
To perform the hypothesis test, we would calculate the z-test statistic using the formula:
z = (μ - μ0) / (σ / √n),
where μ is the sample mean, μ0 is the population mean under the null hypothesis, σ is the population standard deviation, and n is the sample size.
Using the given data: μ = 9.5, μ0 = 6, σ = 7.6, and n = 16, the z-test statistic is calculated to determine if there is enough evidence to reject the null hypothesis in favor of the alternative.
After calculating z, we compare it to the critical value from the z-table at α = 0.03. If the calculated z-value is greater than the critical value, we reject H0 and conclude that the average wait time is indeed greater than 6 minutes.