Question

According to the National Automobile Dealers Association, the mean price for used cars is $10,192. A manager of kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine wether the population mean price for used cars at this particular dealership differed from the national mean.

The sample mean price was $9,750 and the sample standarddeviation was $1,400.
A. Formulate the hypotheses that can be used to determine wether a difference exists in the mean price for used cars at the dealership.
B. What is the p-value?
C. At α = .05, what is your conclusion?

Answer 1

We have formulated the null and alternative hypotheses for testing whether there's a difference in the mean price for used cars at the Kansas City dealership from the national mean. The p-value can't be provided without conducting the actual hypothesis test. At a significance level of 0.05, the null hypothesis is rejected if the p-value is less than 0.05, otherwise it is not rejected.

Step-by-step explanation:

To determine whether the mean price for used cars at the Kansas City dealership differs from the national mean of $10,192, we can formulate the following hypotheses:

• The null hypothesis (H0): μ = $10,192, which indicates that there is no difference between the national mean and the dealership's mean price.
• The alternative hypothesis (H1): μ ≠ $10,192, signifying that there is a difference between the national mean and the dealership's mean price.

The p-value is a probability that measures the evidence against the null hypothesis. Without specific test statistics, such as the t-score, and without conducting the actual hypothesis test using the sample data, it is impossible to provide the p-value.

For concluding the hypothesis test at a significance level (α) of 0.05, you would compare the p-value to α. If the p-value is less than α, you reject the null hypothesis since there is sufficient evidence to support a significant difference between the dealership's mean price and the national mean. If the p-value is greater than α, you would fail to reject the null hypothesis since there is insufficient evidence to conclude a significant difference.