An online used car company sells second-hand cars. For 30 randomly selected tran

Question

An online used car company sells second-hand cars. For 30 randomly selected transactions, the mean price is 2900 dollars.

Part a) Assuming a population standard deviation transaction prices of 220 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.

Part b)
Which of the following (multiple possble) 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

Explanation / Answer

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
              
X = sample mean =    2900          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    220          
n = sample size =    30          
              
Thus,              
              
Lower bound =    2796.538414          
Upper bound =    3003.461586          
              
Thus, the confidence interval is              
              
(2796.54   ,   3003.46) [ANSWER]

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B.

It is

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

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