A major car manufacturer wants to test a new engine to determine whether it meets new air pollution standards. The
mean emission of all engines of this type must be lower than 20 parts per million of carbon. A number of engines are manufactured for testing purposes, and the emission level of each is determined. The data (in parts per million) are listed below:
15.6, 16.2, 22.5, 20.5, 16.4, 19.4, 16.6, 17.9, 12.7, 13.9
a). At 5% level of significance, is there sufficient evidence to allow the manufacturer to conclude that this type of engine meets the pollution standard? Your conclusion must be in terms of the P-Value as well as setting up a Rejection Region. You must show all necessary work.
b). Which statistical distribution should be applied in this situation and why? Explain carefully.
c). Knowing that a significant amount of capital investment were required to manufacture the engine, what, if anything, does the manufacturer have to be concerned about with respect to the conclusion of part (a)? Explain carefully
d). Based on a 95% confidence level, estimate the mean emission of all engines.
e). Carefully interpret this interval estimation.
f). Explain carefully whether or not there is sufficient evidence to allow the manufacturer to conclude that this type of engine meets the pollution standard using the estimation in part (d).