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A research engineer for a tire manufacturer is investigating tire life for a new rubber compound. She has built
10 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 61,492 and
3035 kilometers, respectively.
(a) The engineer would like to demonstrate that the mean life of this new tire is in excess of 60,000 km. Test appropriate hypotheses, being sure to state assumptions, and draw conclusions. Use ?=0.05.
(b) Suppose that the mean life is as long as 61,000 km, what is the probability of type II error?
(c) Suppose that if the mean life is as long as 61,000 km, the engineer would like to detect this difference with probability at least 0.90. What sample size would be required?

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