Aresearch 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. formulate and test appropriate hypotheses, being sure to state (test, if possible) assumptions, and draw conclusions using the p-value approach.
(b) 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. was the sample size n 10 used in part (a) adequate? use the sample standard deviation s as an estimate of σ in reaching your decision.
(c) find a 9596 one-sided lower confidence bound on mean tire life.
(d) use the bound found in part (c) to test the hypothesis.