The makers of the MAGNETIZER Engine Energizer System (EES) claim that it improves gas mileage and reduces emissions in automobiles by using magnetic free energy to increase the amount of oxygen in the fuel for greater combustion efficiency. Following are test results, performed under International and U.S. Government agency standards, on a random sample of 14 vehicles. The data give the carbon monoxide (CO) levels, in parts per million, of each vehicle tested, both before installation of EES and after installation.
The following questions pertaining to the data above I need answered are:
Identify the design of the study.
A. paired t-test of a mean
B. two-sample t-test of means
C. either test will work
Suppose that you want to perform a hypothesis test to determine whether, on average, EES reduces CO emissions.
What null hypothesis would you use to test if the MAGNETIZER reduces emissions?
A. H0: μ (before MAGENTIZER) = μ (after MAGNETIZER)
B. H0: μ (before MAGENTIZER) ≠ μ (after MAGNETIZER)
C. H0: μ d = 0 where μ d = μ (before MAGENTIZER) - μ (after MAGNETIZER)
D. H0: μ d ≠ 0 where μ d = μ (before MAGENTIZER) - μ (after MAGNETIZER)
Suppose that you want to perform a hypothesis test to determine whether, on average, EES reduces CO emissions.
What alternative hypothesis would you use to test if the MAGNETIZER reduces emissions?
A. HA: μ (before MAGENTIZER) = μ (after MAGNETIZER)
B. HA: μ (before MAGENTIZER) > μ (after MAGNETIZER)
C. HA: μ d > 0 where μ d = μ (before MAGENTIZER) - μ (after MAGNETIZER)
D. HA: μ d ≠ 0 where μ d = μ (before MAGENTIZER) - μ (after MAGNETIZER)
E. HA: μ d < 0 where μ d = μ (before MAGENTIZER) - μ (after MAGNETIZER)
Using the data provided, conduct the hypothesis test. What p-value do you obtain?
A. 0.0062
B. 0.0039
C. 0.9961
D. 0.0148
Using the p-value you obtained in the previous question and assuming that you are testing at the 0.01 significance level, what is your conclusion?
A. Reject HO: The MAGNETIZER appears to reduce emissions
B. Reject HO: The MAGNETIZER does not appear to reduce emissions
C. Do not reject HO: The MAGNETIZER appears to reduce emissions
D. Do not reject HO: The MAGNETIZER does not appear to reduce emissions
What is the lower bound for the 99% confidence interval for the change in emissions following the installation of the MAGENTIZER system (before - after)? Show two decimal places in your answer
What is the upper bound for the 99% confidence interval for the change in emissions following the installation of the MAGENTIZER system (before - after)? Show two decimal places in your answer
B. two-sample t-test of means
C. H0: ì d = 0 where ì d = ì (before MAGENTIZER) - ì (after MAGNETIZER)
B. 0.0039
D. Do not reject HO: The MAGNETIZER does not appear to reduce emissions
To answer these questions, we need to consider the design of the study, the null and alternative hypotheses, perform a hypothesis test, calculate the p-value, and then interpret the results by making a conclusion and finding the confidence interval.
1. Design of the study:
The study design in this case is a paired t-test of means because the data given consists of the carbon monoxide (CO) levels measured both before and after the installation of the MAGNETIZER Engine Energizer System (EES) in the same set of 14 vehicles.
2. Null hypothesis for testing if the MAGNETIZER reduces emissions:
The appropriate null hypothesis to test if the MAGNETIZER reduces emissions is H0: μd = 0, where μd is the mean difference in CO levels (before - after MAGNETIZER).
3. Alternative hypothesis for testing if the MAGNETIZER reduces emissions:
The correct alternative hypothesis to test if the MAGNETIZER reduces emissions is HA: μd < 0, where μd is the mean difference in CO levels (before - after MAGNETIZER).
4. Conducting the hypothesis test:
To perform the hypothesis test, we would use the provided data to calculate the t-statistic and find the corresponding p-value. Without the data, it is not possible to calculate the exact p-value required to answer this question.
5. Obtaining the p-value:
Since the data is not provided, we cannot calculate the p-value.
6. Conclusion based on the p-value:
Since we do not have the p-value, we cannot make a conclusion based on it.
7. Lower bound of the 99% confidence interval for the change in emissions:
To calculate the lower bound of the 99% confidence interval, we would need the mean difference and the standard deviation of the differences in CO levels. Without the data, it is not possible to calculate the confidence interval for this question.
8. Upper bound of the 99% confidence interval for the change in emissions:
Similarly, without the data, we cannot calculate the upper bound of the 99% confidence interval for the change in emissions.
In summary, without the actual data, it is not possible to answer the questions regarding the specific values and results. However, by understanding the concepts and methods mentioned above, one can apply them to the given data to obtain the desired answers.