You want to purchase one of the new Altimas. You randomly select 400 dealerships across the United States and find a mean of \$25,000 and sample standard deviation of \$2500. Construct and interpret a 94% confidence interval for the true mean price for the new Nissan Altima.

• A. (24996.25, 25003.75); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24996.25 and \$25003.75.
• B. (24999.25, 25000.24); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24999.25 and \$25000.24.
• C. (24984.912, 25015.088); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24984.912 and \$25015.088.
• D. (24764.25, 25235.75); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24764.25 and \$25235.75.

Answer: (D)

Verified step by step guidance

1. Identify the sample mean (\( \bar{x} \)) and sample standard deviation (\( s \)) from the problem. Here, \( \bar{x} = 25000 \) and \( s = 2500 \).
2. Determine the sample size (\( n \)), which is given as 400 dealerships.
3. Select the confidence level, which is 94%. This will help you find the critical value (\( z^* \)) from the standard normal distribution table.
4. Calculate the standard error of the mean (SEM) using the formula: \( \text{SEM} = \frac{s}{\sqrt{n}} \).
5. Construct the confidence interval using the formula: \( \bar{x} \pm z^* \times \text{SEM} \). This will give you the range within which the true mean price is expected to fall with 94% confidence.