Question

question 3 (1 point)
an online used car company sells second - hand cars. for 30 randomly selected transactions, the mean price is 3000 dollars. assuming a population standard deviation transaction prices of 160 dollars, obtain a 99% confidence interval for the mean price of all transactions. which of the following is a correct interpretation for the 99% confidence interval for the mean price of all transactions.
there is a 99% chance that the mean price of all transactions lies in the interval.
we can be 99% confident that the mean price for this sample of 30 transactions lies in the interval.
99% of their mean sales price lies inside this interval.
we can be 99% confident that all of the cars they sell have a price inside this interval.
question 4 (1 point)

Explanation:

Step1: Recall confidence - interval interpretation

A confidence interval for the population mean gives us a range of values. We are $C\%$ confident that the true population mean lies within this interval. Here, $C = 99$.

Step2: Analyze each option

• Option 1: "There is a 99% chance that the mean price of all transactions lies in the interval." This is a correct interpretation. A 99% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 99% of those intervals would contain the true population mean.
• Option 2: "We can be 99% confident that the mean price for this sample of 30 transactions lies in the interval." The confidence - interval is for the population mean, not the sample mean. The sample mean is used to calculate the confidence interval, but the interval is about the population mean. So this is incorrect.
• Option 3: "99% of their mean sales price lies inside this interval." This is an incorrect statement. The confidence interval is not about the percentage of sample means within the interval.
• Option 4: "We can be 99% confident that all of the cars they sell have a price inside this interval." The confidence interval is for the population mean price, not for the individual car prices. So this is incorrect.

Answer:

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