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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 μd (where the difference = MPG with Additive X less (or minus) MPG without Additive X) for the population of all such cars was found to be (0.5 MPG, 4.5 MPG).
Question 3 Subquestions
3.a0.5 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.
3.b0.5 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.
3.c0.5 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.
3.d0.5 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.
3.e0.5 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: μd = 1 MPG versus the alternative Ha: μd ≠ 1 MPG, at a 1% level of significance.
Here the parameter μdμ 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
3.f0.5 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: μd = 1.2 MPG versus the alternative Ha: μd ≠ 1.2 MPG, at a 10% level of significance.
Here the parameter μd 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
Question-3aMargin of error = (4.5-0.5)/2=2Question-3bNo, this is not a correct statement as if we repeat study many times than 99% of the interval contains the true mean.Question-3cNo, this is…
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