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

• A. (24992.5, 25007.5); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24992.5 and \$25007.5.
• B. (24882.438, 25117.563); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24882.438 and \$25117.563.
• C. (24764.875, 25235.15); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24764.875 and \$25235.15.
• D. (24529.75, 25470.25); We are 94% confident that the true mean price for the new Nissan Altima falls between \$24529.75 and \$25470.25.

Answer: (C)

Verified step by step guidance

1. Identify the sample mean (\( \bar{x} \)) and the population standard deviation (\( \sigma \)). Here, \( \bar{x} = 25000 \) and \( \sigma = 2500 \).
2. Determine the sample size (\( n \)), which is 400 in this case.
3. Select the confidence level, which is 94%. This will help you find the corresponding z-score from the standard normal distribution table. For a 94% confidence level, the z-score is approximately 1.88.
4. Calculate the standard error of the mean using the formula \( \text{SE} = \frac{\sigma}{\sqrt{n}} \). Substitute \( \sigma = 2500 \) and \( n = 400 \) into the formula.
5. Construct the confidence interval using the formula \( \bar{x} \pm z \times \text{SE} \). Substitute the values for \( \bar{x} \), \( z \), and \text{SE} to find the lower and upper bounds of the confidence interval.