A researcher wanted to study the effect of a newly developed gasoline additive (

Question

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 X versus 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 1 point(s) 1.5 2.5 99 Cannot be determined since we do not know the sample size n 4.b Consider the following statement: 1 points If we were to repeat this study many times, we would expect 99% of the resulting cars to have mileage improve by from 0.5 MPG to 4.5 MPG when using the new Additive Is this a correct statement, and thus, could be used in the report summary? O Yes, this is a correct statement No, this is not a correct statement. 4.c Consider the following statement: 1 point(s) With 99% confidence, we would estimate the mean improvement in mileage with the new Additive X to be 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

Explanation / Answer

Question-4a

Margin of error = (4.5-0.5)/2=2

Question-4b

No, this is not a correct statement as if we repeat study many times then 99% of the interval contains the true mean.

Question-4c

No, this is not a correct statement as if we repeat study many times then 99% of the interval contains the true mean.

Question-4d

No, this is not a correct statement as if we repeat study many times then 99% of the interval contains the true mean(here sample mean is written)

Question-4e

As our 99%cofnidence interval (0.5,4.5) contains unity (“1”) , so we do not reject the nul hypothesis.

Fail to reject the null hypothesis

Question-4f

As our 99% confidence interval (0.5,4.5) contains 1.2 , so we do not reject the null hypothesis.

Fail to reject the null hypothesis

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