A tire manufacturer produces tires that have a mean life of atleast 30000 miles when the production process is working properly.The operations manager stops the production process if there isevidence that the mean tire life is below 30000 miles. The testablehypotheses in this situation are ?0:?=30000 H 0 : μ = 30000 vs??:?<30000 H A : μ < 30000 .

1. Identify the consequences of making a Type I error. A. Themanager does not stop production when it is necessary. B. Themanager does not stop production when it is not necessary. C. Themanager stops production when it is not necessary. D. The managerstops production when it is necessary.

2. Identify the consequences of making a Type II error. A. Themanager does not stop production when it is not necessary. B. Themanager stops production when it is not necessary. C. The managerstops production when it is necessary. D. The manager does not stopproduction when it is necessary. To monitor the production process,the operations manager takes a random sample of 15 tires each weekand subjects them to destructive testing. They calculate the meanlife of the tires in the sample, and if it is less than 28500, theywill stop production and recalibrate the machines. They know basedon past experience that the standard deviation of the tire life is2000 miles.

3. What is the probability that the manager will make a Type Ierror using this decision rule? Round your answer to four decimalplaces.

4. Using this decision rule, what is the power of the test ifthe actual mean life of the tires is 28600 miles? That is, what isthe probability they will reject ?0 H 0 when the actual averagelife of the tires is 28600 miles? Round your answer to four decimalplaces.