Hypothesis Testing We start with an example



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Hypothesis Testing
We start with an example:
Status Quo: A type of automobile engine emits a mean of 100 mg of nitrogen oxides per second at 100 horsepower.

Proprosed alternative: A modification of the engine proposed to reduce the mean emission rate.
The automobile manufacturer will abandon the original engine and adopt the new engine design (at much cost to the manufacturer) if it can be demonstrated that the modified engine has a mean emission rate less than 100 mg/s.
Evidence: A sample of 50 modified engines are built and tested. The sample mean emission is mg/s.

It seems as though that the modification improves things. But does it? The β€œnew” mean emission rate is a parameter of the conceptual population of engines that would be built if the modification were put in place. The β€œ92” is based only on a sample of 50, and so it is only an estimate of .We already know that the sample mean is subject to some uncertainty, and the true mean emission rate might be higher or lower than 92.
The concern is that the actual mean might be 100 or even greater. That is, if they go through all the burden of manufacturing a new type of engine, they find out the mean emission rate is no better, or even worse!
We have two hyopthesis:
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