5. Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil- filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation $\sigma$ of sheath thickness is less than 0.05 mm.
(a) (2 pts) What null and alternative hypotheses should be tested?
$H_0$: ____________________________________, $H_a$: ____________________________________
(b) (1 pt) Is "concluding the variability in thickness is satisfactory when it is not." the type I or type II error?
Type I, Type II
(c) (1 pt) Is "concluding the variability in thickness is not satisfactory when it is." the type I or type II error?
Type I, Type II