A research engineer for a tire manufacturer is investigating tire life for a new

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 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. (c) Find a 95% one-sided lower confidence bound on mean tire life. (d) Use the bound found in part (c) to test the hypothesis.

Explanation / Answer

H0: µ = 60000

H1: µ >60000

Assumptions

Small sample

Normal population

Unkown sd

t = (X-0)/(s/n)

= (61,492 - 60,000)/(3035/10)

= 1.554

There is insufficient evidence to conclude that the mean tire life issignificantly greater than 60000km.

P value

P(T>1.554) = 0.0773

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