Question 4 Background: Additive X plus A researcher wanted to study the effect o

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Question 4 Background: Additive X plus A researcher wanted to study the effect of a newly developed gasoline additive (Additive on automobile mileage (miles per gallon, MPG). To gather information, a random sample of cars has been selected and their gasoline mileages (MPG) have been determined. For each car, the MPG was measured both when gasoline without Additive X is used and when gasoline with Additive X is used. The order of the two treatments (with Additive Xversus without Additive was randomized and care was taken so that there was no carry over effect between the two measurements. The 99% confidence interval for the average improvement in mileage (difference MPG with Additive X less MPG without Additive for the population of all such cars was found to be (0.5 MPG, 4.5 MPG). Question 4 Subquestions 4.a. The margin of error of this interval is point(s) 1.5 99 Cannot be determined since we do not know the sample size n Saved 4.b Consider the following statement: If we were to repeat this study many times, we would expect 99% of the resulting cars to have mileage point(s) Is this a correct statement, and thus, could be used in the report summary? U Yes, this is a correct statement No, this is not a correct statement. Saved 4.c Consider the following statement: With 99% confidence, we would estimate the mean improvement in mileage with the new Additive X to be point(s between 0.5 MPG and 4.5 MPG for the population of all such cars, Is this a correct statement, and thus, could be used in the report summary? Yes, this is a correct statement No, this is not a correct statement. Saved

Explanation / Answer

4a. We know that the range of the confidence interval is defined by the sample statistic +- margin of error.

Here 99% confidence interval is given as (0.5 MPG, 4.5 MPG). From this we can infer that sample statistic is 2.5 and margin of error is 2.

So the margin of error for this interval is 2 MPG.

4b.This is incorrect. Remember that a confidence level describes how likely you are to have gotten a sample that was close enough to the true parameter.

4c. This is incorrect. Remember that a confidence level describes how likely you are to have gotten a sample that was close enough to the true parameter.

4d. This is correct statement. We would expect 99% of the samples to contain the sample mean improvement in mileage.

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