# Statistics

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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

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