An online used car company sells second-hand cars. For 30 randomly selected transactions, the mean price is 2700 dollars. 1) Assuming a population standard deviation transaction prices of 280 dollars, obtain a 99% confidence interval for the mean price of all transactions.  Confidence interval: 2) Which of the following is the correct interpretation for your answer in part (1)? 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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...