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ID: 3065692 • Letter: P
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Previous Problem Problem List Next Problem 1 point) An online used car company sells second-hand cars. For 30 randomly selected transactions, the mean price is 2900 dollars Part a) Assu of all transactions. Ple places ming a population standard deviation transaction prices of 130 dollars, obtain a 99% confidence interval for the mean price ase carry at least three decimal places in intermediate steps. Give your final answer to the nearest two decimal 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. We can be 99% confident that the mean price for this sample of 30 transactions lies in the interval CD C. If we repeat the study many times, 99% of the calculated confidence intervals will contain the mean price of all transactions. D. None of the above Note: You can earn partial credit on this problem. You have attempted this problem 0 times rch DOLLExplanation / Answer
mean= 2900 dollars , n= 30 and population standard deviation is 130 dollars
Since population standard deviation is known we will use Z critical value to get 99% confidence interval.
M = 2900
Zcritcal value of 0.99 confidence level = 2.58
sM = ((130)^2/30) = 23.735
= M ± Z(sM)
= 2900 ± 2.58*23.735
= 2900 ± 61.236
M = 2900, 99% CI [2838.764, 2961.236].
You can be 99% confident that the population mean () falls between 2838.76 and 2961.24
Interpretation of 99% confidence interval. if repeated samples were taken and the 99% confidence interval was computed for each sample, 99% of the intervals would contain the population mean.
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