A manufacturer of machine bearings claims that \(90 \%\) of the heavy machine bearings have a work life of more than 5 years. You doubt this claim and want to refute it on the basis of a sample of 200 bearings where 170 did work for more than 5 years. First,

(a) Conduct a test of hypotheses using \(\alpha=0.10\).

(b) In light of your discussion in part (a), what error could you have made? Explain in the context of this exercise.