Final answer:
To determine if there's a difference in used car prices at a dealership compared to the national mean, we formulate null (H0: μ = $10,550) and alternative (Ha: μ ≠ $10,550) hypotheses, calculate the p-value using a statistical test, and compare it to a 0.05 significance level (alpha) to reach a conclusion.
Step-by-step explanation:
In addressing the question related to the mean price for used cars at a Kansas City dealership and comparing it to the national mean, we are dealing with a hypothesis testing scenario in statistics. Here's how to tackle the given problem:
Formulate the Hypotheses
The null hypothesis (H0) would state that there is no difference between the mean price for used cars at the dealership and the national average, which is $10,550. Therefore, H0: μ = $10,550. The alternative hypothesis (Ha) would suggest that there is a difference, so Ha: μ ≠ $10,550.
Calculate the p-value
The p-value is calculated based on the sample mean, the sample standard deviation, and the size of the sample using the appropriate statistical test, often a t-test for a single sample.
Conclusion at α = .05
If the p-value is less than the significance level (alpha) of 0.05, we reject the null hypothesis, indicating that there is a statistically significant difference between the dealership's mean price for used cars and the national mean. If it is higher, we fail to reject the null hypothesis.