An online used car company sells second-hand cars. For 30 randomly selected transactions, the mean price is 2300 dollars.

Question

An online used car company sells second-hand cars. For 30 randomly selected transactions, the mean price is 2300 dollars.

Part a) Assuming a population standard deviation transaction prices of 290 dollars, obtain a 99% confidence interval for the mean price of all transactions. Please carry at least three decimal places in intermediate steps. Give your final answer to the nearest two decimal places.

Confidence interval: (____,____)

Part b)

Which of the following is the correct interpretation for your answer in part (a)?

A. There is a 99% chance that the mean price of all transactions lies in the interval

B. If we repeat the study many times, 99% of the calculated confidence intervals will contain the mean price of all transactions.

C. We can be 99% confident that the mean price for this sample of 30 transactions lies in the interval

D. None of the above

Answer 1

CI = sample mean +/- z-critical * standard deviation/square root (sample size)

z-critical is z-score corresponding to 0.995 probability.

For part b), the correct answer is B.