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 X) 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 X) 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 X) for the population of all such cars was found to be (0.5 MPG, 4.5 MPG).

Question 4 Subquestions

4.a

1 point(s)

The margin of error of this interval is:

1

1.5

2

2.5

99

Cannot be determined since we do not know the sample size n.

4.b

1 point(s)

Consider the following statement:
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 X.
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.

4.c

1 point(s)

Consider the following statement:
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.

4.d

1 point(s)

Consider the following statement:
If we were to repeat this study many times, we would expect 99% of the resulting intervals to contain the sample mean improvement in mileage (with Additive X versus without Additive X).
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.

4.e

1 point(s)

A competitor’s fuel additive had an established average improvement in mileage of 1 MPG. The researcher would like to use the confidence interval to test the hypotheses H0: = 1 MPG versus the alternative Ha: 1 MPG, at a 1% level of significance.
Here the parameter represents the mean improvement in mileage (with Additive X versus without Additive X) for the population of all such cars (i.e., the researcher is testing the hypotheses whether the population mean mileage improvement with Additive X is different from that with the competitior's fuel additive).
What would be her decision?

reject the null hypothesis

fail to reject the null hypothesis

cannot be determined

4.f

1 point(s)

Another competitor’s fuel additive had an established average improvement in mileage of 1.2 MPG. The researcher would like to use the confidence interval to test the hypotheses H0: = 1.2 MPG versus the alternative Ha: 1.2 MPG, at a 10% level of significance.
Here the parameter represents the mean improvement in mileage (with Additive X versus without Additive X) for the population of all such cars (i.e., the researcher is testing the hypotheses whether the population mean mileage improvement with Additive X is different from that with another competitior's fuel additive).
What would be her decision?

reject the null hypothesis

fail to reject the null hypothesis

cannot be determined

Explanation / Answer

1a. Here LCL=0.5 and UCL=4.5

Mean-Margin of Error=0.5

Mean+ margin of error=4.5

Solving this we get mean=5/2=2.5

Putting this in LCL E=2.5-0.5=2

Now to find b,C and d let's u understand what CI means

confidence interval is a range of values so defined that there is a specified probability that the value of a parameter lies within it. Based on this answers are below

b. No this is not a correct statement

c. Yes, this is a correct statement

d. No this is not a correct statement

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