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Hw9_solutions_to_POST - 8 Devore Sec 8.1(p.324-325 3 Ho =...

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8) Devore Sec 8.1 (p.324-325) # 3 : H o : μ = 100 H a : μ > 100 In this formulation, H o states the welds do not conform to specification. This assertion will not be rejected unless there is strong evidence to the contrary. Thus if the null hypothesis is rejected, the alternate must be assumed, which is equivalent to saying that the welds satisfy the specification. Thus H a : μ > 100 must be the case, or the welds can never be proven to meet the specification. Using H a : 100 < μ results in the welds being believed in conformance unless provided otherwise, so the burden of proof is on the non-conformance claim. # 4 : When the alternative is H a : 5 < μ (safe), the formulation is such that the water is believed unsafe until proved otherwise. A type I error involved deciding that the water is safe (rejecting H o ) when it isn’t (H o is true). This is a very serious error, so a test which ensures that this error is highly unlikely is desirable. A type II error involves judging the water unsafe when it is actually safe.
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