Before agreeing to purchase a large order of polyethylene sh

Before agreeing to purchase a large order of polyethylene sheaths for a particular type of highpressure
oil-filled submarine power cable, a company wants to see conclusive evidence that the
true standard deviation of sheath thickness is less than .05 mm. What hypotheses should be
tested, and why? In this context, what are the type I and type II errors?

Solution

Ho : SD < 0.05

H1 : SD >= 0.05

type I error

reject Ho when Ho is true in this context reject that SD is less than 0.05 when actually SD is less than 0.05

Type II error

Accept Ho when its false in this context accept that SD is less than 0.05 but it is false