(Vehicle emissions) The Federal Clean Air Act requires that before a new fuel or fuel additive is sold in the United States, the producer must demonstrate that the emission products generated will not cause a vehicle to fail to achieve compliance with certified emission standards. To estimate the difference in emission levels, the US. Environmental Protection Agency (EPA) requires, among other tests, a \"matched-pair" test in which a random sample of cars is driven once with a standard fuel and then once with the new fuel. For each car, the difference between emissions with new fuel and emissions with stan- dard fuel is computed. You may assume that this difference is approximately normally distributed. 1f the average difference yields a statistically signifi- cant increase in emissions with the new fuel {at the 5% signicance level}, the new fuel fails the test. The data below on the next page show the nitrous oxide (NOx) emissions for sixteen cars driven first once with a standard fuel and once with Petrocoal, a gasoline with a methanol additive. (a) Does Petrocoal pass the test? (b) Suppose you ignored the fact that the data are in the form of matched pairs, and instead treated them as two independent samples. Would Petrocoal pass the test? What is the reason for the difference in the re- sults? Which form of the test is preferable, and why? You can assume the variance in the two populations (cars operating with Petrocoal and cars operating with standard fuel) is the same