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. [SOURCE: Global Source Marketing.]
Suppose that you want to perform a hypothesis test to determine whether, on average, EES reduces CO emissions.
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?
Inadequate data.
To perform a hypothesis test to determine whether, on average, EES reduces CO emissions, there are several steps involved:
1. State the null hypothesis (H0) and alternative hypothesis (Ha):
- Null hypothesis (H0): The EES does not reduce CO emissions (μd = 0).
- Alternative hypothesis (Ha): The EES reduces CO emissions (μd < 0, where μd represents the population mean difference of CO emissions).
2. Choose the significance level (α): In this case, the significance level is given as 0.01.
3. Calculate the test statistic: The test statistic for this hypothesis test is a t-statistic. However, since the question specifies using the p-value obtained in the previous question, we don't need to calculate the test statistic again.
4. Determine the p-value: The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true. In the previous question, the p-value was obtained, but it is not provided in this question.
5. Compare the p-value with the significance level: If the p-value is less than the significance level (α), then we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Since the p-value is not provided in this question, we cannot directly determine the conclusion based on it. However, if the p-value obtained in the previous question was less than 0.01 (the significance level specified), then we can conclude that there is evidence to suggest that EES reduces CO emissions. On the other hand, if the p-value was greater than or equal to 0.01, we fail to reject the null hypothesis.
Please provide the p-value obtained in the previous question for a more specific conclusion.