A research engineer for a tire manufacturer is investigating tire life for a new rubber compound....
Question:
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 3,035 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 {eq}\alpha {/eq} = 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?
Hypothesis testing:
Single sample t-test is used when we have not any information about the population standard deviation so we took the sample and then use sample standard deviation to calculate the t-test. The type II error gives the probability of accepting the null hypothesis when it is false.
Answer and Explanation: 1
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{eq}\begin{align*} {\rm{Number}}\,{\rm{of tires}},n &= 10\\ \bar X &= 61492\\ S &= 3035 \end{align*} {/eq}
(a)
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